doane - stat - chap 006

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Chapter 06 Discrete Probability Distributions True / False Questions 1. A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment. True False 2. A discrete random variable has a countable number of distinct values. True False 3. The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities. True False 4. A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF). True False

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Doane - Stat 2 - Chapter 6 Test answer key

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Chapter 06Discrete Probability Distributions

True / False Questions1.A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment.TrueFalse

2.A discrete random variable has a countable number of distinct values.TrueFalse

3.The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities.TrueFalse

4.A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF).TrueFalse

5.A random variable may be discrete or continuous, but not both.TrueFalse

6.To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.TrueFalse

7.The outcomes for the sum of two dice can be described as a discrete uniform distribution.TrueFalse

8.A discrete binomial distribution is skewed right when > .50.TrueFalse

9.When = .70 the discrete binomial distribution is negatively skewed.TrueFalse

10.The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.TrueFalse

11.The Poisson distribution can be skewed either left or right, depending on .TrueFalse

12.Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.TrueFalse

13.As a rule of thumb, the Poisson distribution can be used to approximate a binomial distribution when n 20 and .05.TrueFalse

14.The hypergeometric distribution is skewed right.TrueFalse

15.The hypergeometric distribution assumes that the probability of a success remains the same from one trial to the next.TrueFalse

16.The hypergeometric distribution is not applicable if sampling is done with replacement.TrueFalse

17.As a rule of thumb, the binomial distribution can be used to approximate the hypergeometric distribution whenever the population is at least 20 times as large as the sample.TrueFalse

18.An example of a geometric random variable is the number of pine trees with pine beetle infestation in a random sample of 15 pine trees in Colorado.TrueFalse

19.Calculating the probability of getting three aces in a hand of five cards dealt from a deck of 52 cards would require the use of a hypergeometric distribution.TrueFalse

20.The Poisson distribution is appropriate to describe the number of babies born in a small hospital on a given day.TrueFalse

21.The gender of a randomly chosen unborn child is a Bernoulli event.TrueFalse

22.The Poisson distribution has only one parameter.TrueFalse

23.The standard deviation of a Poisson random variable is the square root of its mean.TrueFalse

24.Customer arrivals per unit of time would tend to follow a binomial distribution.TrueFalse

25.The two outcomes (success, failure) in the Bernoulli model are equally likely.TrueFalse

26.The expected value of a random variable is its mean.TrueFalse

Multiple Choice Questions27.A discrete probability distribution:

A.is a listing of all possible values of the random variable.

B.assigns a probability to each possible value of the random variable.

C.can assume values between -1 and +1.

D.is independent of the parameters of the distribution.

28.The number of male babies in a sample of 10 randomly chosen babies is a:

A.continuous random variable.

B.Poisson random variable.

C.binary random variable.

D.binomial random variable.

29.A discrete random variable:

A.can be treated as continuous when it has a large range of values.

B.cannot be treated as continuous.

C.is best avoided if at all possible.

D.is usually uniformly distributed.

30.Which is not a discrete random variable?

A.The number of defects in a 4 8 sheet of plywood

B.The number of female passengers who board a plane

C.The time until failure of a vehicle headlamp

D.The number of correct answers on a statistics exam

31.Which is a not a discrete random variable?

A.The number of births in a hospital on a given day

B.The number of fives obtained in four rolls of a die

C.The hourly earnings of a call center employee in Boston

D.The number of applicants applying for a civil service job

32.Which statement is incorrect?

A.The Poisson distribution is always skewed right.

B.The binomial distribution may be skewed left or right.

C.The discrete uniform distribution is always symmetric.

D.The hypergeometric distribution is symmetric.

33.The random variable X is the number of shots it takes before you make the first free throw in basketball. Assuming the probability of success (making a free throw) is constant from trial to trial, what type of distribution does X follow?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

34.Which probability model is most nearly appropriate to describe the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes, assuming a constant probability of a burned-out tube?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

35.Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

36.Which model would you use to describe the probability that a call-center operator will make the first sale on the third call, assuming a constant probability of making a sale?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

37.In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

38.Which model best describes the number of nonworking web URLs ("This page cannot be displayed") you encounter in a randomly chosen minute while surfing websites for Florida vacation rental condos?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

39.Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

A.Poisson

B.Hypergeometric

C.Binomial

D.Uniform

40.Which model best describes the number of incorrect fare quotations by a well-trained airline ticket agent between 2 p.m. and 3 p.m. on a particular Thursday.

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

41.Which model best describes the number of blemishes per sheet of white bond paper?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

42.To ensure quality, customer calls for airline fare quotations are monitored at random. On a particular Thursday afternoon, ticket agent Bob gives 40 fare quotations, of which 4 are incorrect. In a random sample of 8 of these customer calls, which model best describes the number of incorrect quotations Bob will make?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

43.The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

44.On a particular Thursday in August, 40 Grand Canyon tourists enter a drawing for a free mule ride. Ten of the entrants are European tourists. Five entrants are selected at random to get the free mule ride. Which model best describes the number of European tourists in the random sample?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

45.Which model best describes the number of births in a hospital until the first twins are delivered?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

46.On a randomly chosen Wednesday, which probability model would you use to describe the number of convenience store robberies in Los Angeles?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

47.Which probability model would you use to describe the number of customers served at a certain California Pizza Kitchen until the first customer orders split pea soup?

A.Binomial

B.Geometric

C.Uniform

D.Poisson

48.Which distribution has a mean of 5?

A.Poisson with = 25.

B.Binomial with n = 200, = .05

C.Hypergeometric with N = 100, n = 10, s = 50

49.Of the following, the one that most resembles a Poisson random variable is the number of:

A.heads in 200 flips of a fair coin.

B.annual power failures at your residence.

C.face cards in a bridge hand of 13 cards.

D.defective CDs in a spool containing 15 CDs.

50.A charity raffle prize is $1,000. The charity sells 4,000 raffle tickets. One winner will be selected at random. At what ticket price would a ticket buyer expect to break even?

A.$0.50

B.$0.25

C.$0.75

D.$1.00

51.A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If it rolls to a 4, 5, or 6 you lose $1. Find the expected winnings.

A.$0.50

B.$3.00

C.$1.50

D.$1.00

52.A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6 you lose $1. Find the expected winnings.

A.$0.00

B.$1.00

C.$0.50

D.$0.25

53.A carnival has a game of chance: a fair coin is tossed. If it lands heads you win $1.00 and if it lands tails you lose $0.50. How much should a ticket to play this game cost if the carnival wants to break even?

A.$0.25

B.$0.50

C.$0.75

D.$1.00

54.Ephemeral Services Corporation (ESCO) knows that nine other companies besides ESCO are bidding for a $900,000 government contract. Each company has an equal chance of being awarded the contract. If ESCO has already spent $100,000 in developing its bidding proposal, what is its expected net profit?

A.$100,000

B.$90,000

C.-$10,000

D.$0

55.The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?

A.1.2

B.1.0

C.1.5

D.2.0

56.The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that at least 1 student comes to office hours on any given Monday?

A..30

B..40

C..50

D..60

57.The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that fewer than 2 students come to office hours on any given Monday?

A..10

B..40

C..70

D..90

58.The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?

A.1.1

B.1.3

C.1.7

D.1.9

59.Given the following probability distribution, what is the expected value of the random variable X?

A.175

B.150

C.200

D.205

60.Which of the following characterizes a Bernoulli process?

A.A random experiment that has only two outcomes.

B.The probability of "success" varies with each trial.

C.Either outcome has the same chance of occurrence.

D.The "success" must be a desirable outcome.

61.The binomial distribution describes the number of:

A.trials to obtain the first "success" in a Bernoulli process.

B.trials to obtain n "successes" in a Bernoulli process.

C."successes" or "failures" in a Bernoulli process.

D."successes" in n Bernoulli trials.

62.Which of the following is not a requirement of a binomial distribution?

A.Constant probability of success

B.Only two possible Bernoulli outcomes

C.Fixed number of trials

D.Equally likely outcomes

63.The binomial distribution is symmetrical when:

A. = 1 and 1 - = 0.

B. = and 1 - = .

C. = and 1 - = .

D. = 0 and 1 - = 1.

64.The variance will reach a maximum in a binomial distribution when:

A. = 1 and 1 - = 0.

B. = and 1 - = .

C. = and 1 - = .

D. = 0 and 1 - = 1.

65.Which distribution is most strongly right-skewed?

A.Binomial with n = 50, = .70

B.Binomial with n = 50, = .90

C.Binomial with n = 50, = .40

D.Binomial with n = 50, = .10

66.A random variable is binomially distributed with n = 16 and = .40. The expected value and standard deviation of the variables are:

A.2.00 and 1.24

B.4.80 and 4.00

C.6.40 and 1.96

D.2.00 and 1.20

67.The expected value (mean) of a binomial variable is 15. The number of trials is 20. The probability of "success" is:

A..25

B..50

C..75

D..30

68.If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

A..6174

B..3826

C..8131

D..1869

69.In Quebec, 90 percent of the population subscribes to the Roman Catholic religion. In a random sample of eight Quebecois, find the probability that the sample contains at least five Roman Catholics.

A..0050

B..0331

C..9950

D..9619

70.Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?

A..2055

B..2362

C..7946

D..4417

71.The probability that a visitor to an animal shelter will adopt a dog is .20. Out of nine visits, what is the probability that at least one dog will be adopted?

A..8658

B..3020

C..5639

D..1342

72.Based on experience, 60 percent of the women who request a pregnancy test at a certain clinic are actually pregnant. In a random sample of 12 women, what is the probability that at least 10 are pregnant?

A..0639

B..1424

C..0196

D..0835

73.If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

A..5987

B..3151

C..0116

D..1872

74.Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned?

A..9950

B..9619

C..0331

D..1488

75.The probability that an Oxnard University student is carrying a backpack is .70. If 10 students are observed at random, what is the probability that fewer than 7 will be carrying backpacks?

A..3504

B..2001

C..6177

D..2668

76.An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

A..5615

B..2775

C..7161

D..0388

77.A random variable X is distributed binomially with n = 8 and = 0.70. The standard deviation of the variable X is approximately:

A.0.458

B.2.828

C.1.680

D.1.296

78.Suppose X is binomially distributed with n = 12 and = .20. The probability that X will be less than or equal to 3 is:

A..5584

B..7946

C..2362

D..7638

79.Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and = .25?

A.=BINOM.DIST(RAND(), 16, .25, 0)

B.=BINOM.DIST(0, 16, .25, RAND())

C.=BINOM.INV(16, .25, RAND())

D.=BINOM.INV(0, 16, .25, RAND())

80.A network has three independent file servers, each with 90 percent reliability. The probability that the network will be functioning correctly (at least one server is working) at a given time is:

A.99.9 percent.

B.97.2 percent.

C.95.9 percent.

D.72.9 percent.

81.Which statement concerning the binomial distribution is correct?

A.Its PDF covers all integer values of X from 0 to n.

B.Its PDF is the same as its CDF when = .50.

C.Its CDF shows the probability of each value of X.

D.Its CDF is skewed right when < .50.

82.Historically, 2 percent of the stray dogs in Southfield are unlicensed. On a randomly chosen day, the Southfield city animal control officer picks up seven stray dogs. What is the probability that fewer than two will be unlicensed?

A..8681

B..9921

C..3670

D..0076

83.The domain of X in a Poisson probability distribution is discrete and can include:

A.any real X value.

B.any integer X value.

C.any nonnegative integer X value.

D.any X value except zero.

84.On Saturday morning, calls arrive at TicketMaster at a rate of 108 calls per hour. What is the probability of fewer than three calls in a randomly chosen minute?

A..1607

B..8913

C..2678

D..7306

85.On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade.

A..7408

B..1992

C..1494

D..9502

86.On average, an IRS auditor discovers 4.7 fraudulent income tax returns per day. On a randomly chosen day, what is the probability that she discovers fewer than two?

A..0518

B..0427

C..1005

D..1523

87.On a Sunday in April, dog bite victims arrive at Carver Memorial Hospital at a historical rate of 0.6 victim per day. On a given Sunday in April, what is the probability that exactly two dog bite victims will arrive?

A..0875

B..0902

C..0988

D..0919

88.If tubing averages 16 defects per 100 meters, what is the probability of finding exactly 2 defects in a randomly chosen 10-meter piece of tubing?

A..8795

B..2674

C..3422

D..2584

89.Cars are arriving at a toll booth at a rate of four per minute. What is the probability that exactly eight cars will arrive in the next two minutes?

A.0.0349

B.0.1396

C.0.9666

D.0.0005

90.Arrival of cars per minute at a toll booth may be characterized by the Poisson distribution if:

A.the arrivals are independent.

B.no more than one arrival can occur in a minute.

C.there is only one lane leading to the booth.

D.the mean arrival rate is at least 30.

91.The coefficient of variation for a Poisson distribution with = 5 is:

A.35.2 percent.

B.58.9 percent.

C.44.7 percent.

D.31.1 percent.

92.The coefficient of variation for a Poisson distribution with = 4 is:

A.35.2 percent.

B.58.9 percent.

C.50.0 percent.

D.26.4 percent.

93.For which binomial distribution would a Poisson approximation be unacceptable?

A.n = 30, = 0.02

B.n = 50, = 0.03

C.n = 200, = 0.10

D.n = 500, = 0.01

94.For which binomial distribution would a Poisson approximation be acceptable?

A.n = 60, = 0.08

B.n = 100, = 0.15

C.n = 40, = 0.03

D.n = 20, = 0.20

95.For which binomial distribution would a Poisson approximation not be acceptable?

A.n = 35, = 0.07

B.n = 95, = 0.01

C.n = 80, = 0.02

D.n = 50, = 0.03

96.The true proportion of accounts receivable with some kind of error is .02 for Venal Enterprises. If an auditor randomly samples 200 accounts receivable, what is the approximate Poisson probability that fewer than two will contain errors?

A..1038

B..0916

C..1465

D..0015

97.The probability that a rental car will be stolen is 0.0004. If 3500 cars are rented, what is the approximate Poisson probability that 2 or fewer will be stolen?

A..3452

B..2417

C..5918

D..8335

98.The probability that a customer will use a stolen credit card to make a purchase at a certain Target store is 0.003. If 400 purchases are made in a given day, what is the approximate Poisson probability that 4 or fewer will be with stolen cards?

A..0053

B..0076

C..9923

D..0555

99.The probability that a ticket holder will miss a flight is .005. If 180 passengers take the flight, what is the approximate Poisson probability that at least 2 will miss the flight?

A..9372

B..0628

C..1647

D..2275

100.The probability that a certain daily flight's departure from ORD to LAX is delayed is .02. Over six months, this flight departs 180 times. What is the approximate Poisson probability that it will be delayed fewer than 2 times?

A..4471

B..3028

C..1257

D..1771

101.If X is a discrete uniform random variable ranging from 0 to 12, find P(X 10).

A..1126

B..1666

C..2308

D..2500

102.If X is a discrete uniform random variable ranging from one to eight, find P(X < 6).

A..6250

B..5000

C..7500

D..3750

103.If X is a discrete uniform random variable ranging from one to eight, its mean is:

A.4.0

B.4.5

C.5.0

D.5.5

104.If X is a discrete uniform random variable ranging from 12 to 24, its mean is:

A.18.5.

B.16.0.

C.18.0.

D.19.5.

105.At Ersatz University, the graduating class of 480 includes 96 guest students from Latvia. A sample of 10 students is selected at random to attend a dinner with the Board of Governors. Use the binomial model to obtain the approximate hypergeometric probability that the sample contains at least three Latvian students.

A..3222

B..1209

C..8791

D..6778

106.There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.

A..3087

B..1681

C..3602

D..8319

107.Use the binomial model to find the approximate hypergeometric probability of at least two damaged flash drives in a sample of five taken from a shipment of 150 that contains 30 damaged flash drives.

A.0.9421

B.0.0579

C.0.7373

D.0.2627

108.On a particular day, 112 of 280 passengers on a particular DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding passes. In a random sample of eight passengers, use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

A..2322

B..8263

C..2926

D..5613

109.A clinic employs nine physicians. Five of the physicians are female. Four patients arrive at once. Assuming the doctors are assigned randomly to patients, what is the probability that all of the assigned physicians are female?

A..0397

B..0295

C..0808

D..0533

110.There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs on the third Visa transaction?

A..0192

B..0025

C..0247

D..0200

111.Ten percent of the corporate managers at Axolotl Industries majored in humanities. What is the probability that the first humanities major is the fifth manager you meet?

A..0656

B..8561

C..5904

D..4095

112.Ten percent of the corporate managers at Axolotl Industries majored in humanities. What is the expected number of managers to be interviewed until finding the first one with a humanities major?

A.15

B.20

C.10

D.17

113.When you send out a resume, the probability of being called for an interview is .20. What is the probability that the first interview occurs on the fourth resume that you send out?

A..4096

B..1024

C..2410

D..0016

114.When you send out a resume, the probability of being called for an interview is .20. What is the expected number of resumes you send out until you get the first interview?

A.5

B.7

C.10

D.12

115.When you send out a resume, the probability of being called for an interview is .20. What is the probability that you get your first interview within the first five resumes that you send out?

A..6723

B..1024

C..2410

D..0016

116.There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs within the first 20 Visa transactions?

A..1362

B..4000

C..3324

D..4538

117.There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the expected number of Visa transactions until the first one is rejected?

A.10

B.20

C.50

D.98

118.The geometric distribution best describes:

A.the number of successes in a sample of n trials.

B.the number of trials until the first success.

C.the number of events in a given unit of time.

D.the process of sampling without replacement.

119.The CDF for the geometric distribution shows:

A.the probability of success in a random experiment consisting of n independent trials.

B.the probability that the first success will occur within a given number of trials.

C.the probability that no success will be obtained in a given Bernoulli trial.

D.the probability of more than one success in the first n trials.

120.If the probability of success is .25, what is the probability of obtaining the first success within the first three trials?

A..4218

B..5781

C..1406

D..2228

121.If the probability of success is .30, what is the probability of obtaining the first success within the first five trials?

A..0024

B..8319

C..1681

D..9976

122.A project has three independent stages that must be completed in sequence. The time to complete each stage is a random variable. The expected times to complete the stages are 1 = 23, 2 = 11, 3 = 17. The expected project completion time is:

A.51.

B.23.

C.40.

D.32.

123.A project has 3 independent stages that must be completed in sequence. The time to complete each stage is a random variable. The standard deviations of the completion times for the stages are 1 = 5, 2 = 4, 3 = 6. The standard deviation of the overall project completion time is:

A.8.77

B.15.0

C.14.2

D.9.24

124.A stock portfolio consists of two stocks X and Y. Their daily closing prices are independent random variables with standard deviations X = 2.51 and Y = 5.22. What is the standard deviation of the sum of the closing prices of these two stocks?

A.33.55

B.6.48

C.7.73

D.5.79

125.A stock portfolio consists of two stocks X and Y. Their daily closing prices are correlated random variables with variances X2 = 3.51 and Y2 = 5.22, and covariance XY = -1.55. What is the standard deviation of the sum of the closing prices of these two stocks?

A.5.63

B.7.18

C.8.73

D.2.68

126.The expected value of a random variable X is 140 and the standard deviation is 14. The standard deviation of the random variable Y = 3X - 10 is:

A.42

B.6.48

C.14

D.32

127.The expected value of a random variable X is 10 and the standard deviation is 2. The standard deviation of the random variable Y = 2X - 10 is:

A.2

B.4

C.-10

D.-6

Chapter 06 Discrete Probability Distributions Answer Key

True / False Questions1.A random variable is a function or rule that assigns a numerical value to each outcome in the sample space of a stochastic (chance) experiment.TRUEReview definition of random variable.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-01 Define a discrete random variable.Topic: Discrete Distributions

2.A discrete random variable has a countable number of distinct values.TRUEReview definition of random variable.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-01 Define a discrete random variable.Topic: Discrete Distributions

3.The expected value of a discrete random variable E(X) is the sum of all X values weighted by their respective probabilities.TRUEReview definition of expected value.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

4.A discrete distribution can be described by its probability density function (PDF) or by its cumulative distribution function (CDF).TRUEReview definition of PDF and CDF.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-03 Define probability distribution; PDF; and CDF.Topic: Discrete Distributions

5.A random variable may be discrete or continuous, but not both.TRUEReview definition of discrete and continuous.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-01 Define a discrete random variable.Topic: Discrete Distributions

6.To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.FALSENot all X values would be equally likely (Poisson distribution would be better).

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

7.The outcomes for the sum of two dice can be described as a discrete uniform distribution.FALSEThe sum of two uniforms is a triangular distribution, as shown in the textbook example.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-04 Know the mean and variance of a uniform discrete model.Topic: Uniform Distribution

8.A discrete binomial distribution is skewed right when > .50.FALSEMost outcomes would be on the right, so a longer left tail exists.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

9.When = .70 the discrete binomial distribution is negatively skewed.TRUEMost outcomes would be on the right, so a longer left tail exists.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

10.The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.TRUEPoisson describes events per unit of time.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

11.The Poisson distribution can be skewed either left or right, depending on .FALSEPoisson is always right-skewed.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

12.Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.TRUEAlthough always right-skewed, the Poisson approaches a normal as the mean increases.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

13.As a rule of thumb, the Poisson distribution can be used to approximate a binomial distribution when n 20 and .05.TRUEThe Poisson is a better approximation to binomial when n is large and is small.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

14.The hypergeometric distribution is skewed right.FALSEThe hypergeometric is skewed right if s/N < .50 (and conversely).

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

15.The hypergeometric distribution assumes that the probability of a success remains the same from one trial to the next.FALSEThe point of the hypergeometric is that is not constant.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

16.The hypergeometric distribution is not applicable if sampling is done with replacement.TRUEThe hypergeometric is used when there is no replacement in sampling from a finite population

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

17.As a rule of thumb, the binomial distribution can be used to approximate the hypergeometric distribution whenever the population is at least 20 times as large as the sample.TRUEThe rule is to use the approximation if n/N < .05.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

18.An example of a geometric random variable is the number of pine trees with pine beetle infestation in a random sample of 15 pine trees in Colorado.FALSEThis is a binomial experiment, assuming is constant.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

19.Calculating the probability of getting three aces in a hand of five cards dealt from a deck of 52 cards would require the use of a hypergeometric distribution.TRUEThis is a hypergeometric experiment (no replacement).

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

20.The Poisson distribution is appropriate to describe the number of babies born in a small hospital on a given day.TRUEEvents per unit of time with no clear upper limit.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

21.The gender of a randomly chosen unborn child is a Bernoulli event.TRUETwo outcomes (0 or 1).

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Bernoulli Distribution

22.The Poisson distribution has only one parameter.TRUEThe one parameter is the mean.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

23.The standard deviation of a Poisson random variable is the square root of its mean.TRUEReview Poisson model.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

24.Customer arrivals per unit of time would tend to follow a binomial distribution.FALSEThis would be a Poisson (arrivals per unit of time).

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

25.The two outcomes (success, failure) in the Bernoulli model are equally likely.FALSEThe probability of success need not be .50.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Bernoulli Distribution

26.The expected value of a random variable is its mean.TRUEThe mean is another name for expected value.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

Multiple Choice Questions27.A discrete probability distribution:

A.is a listing of all possible values of the random variable.

B.assigns a probability to each possible value of the random variable.

C.can assume values between -1 and +1.

D.is independent of the parameters of the distribution.

A discrete PDF assigns a probability to each X value.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-03 Define probability distribution; PDF; and CDF.Topic: Discrete Distributions

28.The number of male babies in a sample of 10 randomly chosen babies is a:

A.continuous random variable.

B.Poisson random variable.

C.binary random variable.

D.binomial random variable.

Constant probability of success in n trials.

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Binomial Distribution

29.A discrete random variable:

A.can be treated as continuous when it has a large range of values.

B.cannot be treated as continuous.

C.is best avoided if at all possible.

D.is usually uniformly distributed.

Review definitions of discrete distributions.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-01 Define a discrete random variable.Topic: Discrete Distributions

30.Which is not a discrete random variable?

A.The number of defects in a 4 8 sheet of plywood

B.The number of female passengers who board a plane

C.The time until failure of a vehicle headlamp

D.The number of correct answers on a statistics exam

Time is continuous.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-01 Define a discrete random variable.Topic: Discrete Distributions

31.Which is a not a discrete random variable?

A.The number of births in a hospital on a given day

B.The number of fives obtained in four rolls of a die

C.The hourly earnings of a call center employee in Boston

D.The number of applicants applying for a civil service job

Someone's earnings would be more like a continuous measurement.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-01 Define a discrete random variable.Topic: Discrete Distributions

32.Which statement is incorrect?

A.The Poisson distribution is always skewed right.

B.The binomial distribution may be skewed left or right.

C.The discrete uniform distribution is always symmetric.

D.The hypergeometric distribution is symmetric.

Review characteristics of the distributions. A hypergeometric is symmetric only if s/N = .50.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

33.The random variable X is the number of shots it takes before you make the first free throw in basketball. Assuming the probability of success (making a free throw) is constant from trial to trial, what type of distribution does X follow?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Geometric model describes the number of trials until the first success.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Geometric Distribution (Optional)

34.Which probability model is most nearly appropriate to describe the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes, assuming a constant probability of a burned-out tube?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

n = 12 Bernoulli trials with fixed probability of success would be a binomial model.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Binomial Distribution

35.Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Events per unit of time with no clear upper limit would resemble a Poisson distribution.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

36.Which model would you use to describe the probability that a call-center operator will make the first sale on the third call, assuming a constant probability of making a sale?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Geometric describes the number of trials to first success.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Geometric Distribution (Optional)

37.In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Events per unit of time with no clear upper limit would resemble a Poisson distribution.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

38.Which model best describes the number of nonworking web URLs ("This page cannot be displayed") you encounter in a randomly chosen minute while surfing websites for Florida vacation rental condos?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Events per unit of time with no clear upper limit would resemble a Poisson distribution.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

39.Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

A.Poisson

B.Hypergeometric

C.Binomial

D.Uniform

Sampling (n = 4 printers) without replacement with known number of "successes" (s = 3 damaged printers) in the population (N = 28 printers).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Hypergeometric Distribution

40.Which model best describes the number of incorrect fare quotations by a well-trained airline ticket agent between 2 p.m. and 3 p.m. on a particular Thursday.

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Events per unit of time with no clear upper limit would resemble a Poisson distribution.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

41.Which model best describes the number of blemishes per sheet of white bond paper?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Events per unit of area with no clear upper limit would resemble a Poisson distribution.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

42.To ensure quality, customer calls for airline fare quotations are monitored at random. On a particular Thursday afternoon, ticket agent Bob gives 40 fare quotations, of which 4 are incorrect. In a random sample of 8 of these customer calls, which model best describes the number of incorrect quotations Bob will make?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Sampling (n = 8 calls selected) without replacement with known number of "successes" (s = 4 incorrect quotes) in the population (N = 40 quotes).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Hypergeometric Distribution

43.The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Independent events per unit of time with no clear upper limit would be Poisson.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

44.On a particular Thursday in August, 40 Grand Canyon tourists enter a drawing for a free mule ride. Ten of the entrants are European tourists. Five entrants are selected at random to get the free mule ride. Which model best describes the number of European tourists in the random sample?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Sampling (n = 5 tourists selected) without replacement with known number of "successes" (s = 10 Europeans) in the population (N = 40).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Hypergeometric Distribution

45.Which model best describes the number of births in a hospital until the first twins are delivered?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Geometric distribution describes the number of trials until the first success.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Geometric Distribution (Optional)

46.On a randomly chosen Wednesday, which probability model would you use to describe the number of convenience store robberies in Los Angeles?

A.Binomial

B.Poisson

C.Hypergeometric

D.Geometric

Events per unit of time with no clear upper limit.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Poisson Distribution

47.Which probability model would you use to describe the number of customers served at a certain California Pizza Kitchen until the first customer orders split pea soup?

A.Binomial

B.Geometric

C.Uniform

D.Poisson

Geometric distribution describes the number of trials until the first success.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-10 Select an appropriate discrete probability distribution from problem context.Topic: Geometric Distribution (Optional)

48.Which distribution has a mean of 5?

A.Poisson with = 25.

B.Binomial with n = 200, = .05

C.Hypergeometric with N = 100, n = 10, s = 50

Review model parameters. The hypergeometric mean is ns/N = (10)(50)/100 = 5.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

49.Of the following, the one that most resembles a Poisson random variable is the number of:

A.heads in 200 flips of a fair coin.

B.annual power failures at your residence.

C.face cards in a bridge hand of 13 cards.

D.defective CDs in a spool containing 15 CDs.

Independent arrivals per unit of time with no clear upper limit would be Poisson.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

50.A charity raffle prize is $1,000. The charity sells 4,000 raffle tickets. One winner will be selected at random. At what ticket price would a ticket buyer expect to break even?

A.$0.50

B.$0.25

C.$0.75

D.$1.00

Expected winning is (1/4000) $1000 = $0.25.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

51.A die is rolled. If it rolls to a 1, 2, or 3 you win $2. If it rolls to a 4, 5, or 6 you lose $1. Find the expected winnings.

A.$0.50

B.$3.00

C.$1.50

D.$1.00

E(X) = (3/6) $2 + (3/6) (-$1) = $0.50.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

52.A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6 you lose $1. Find the expected winnings.

A.$0.00

B.$1.00

C.$0.50

D.$0.25

E(X) = (2/6) $2 + (4/6) (-$1) = $0.6667 - $0.6667 = 0.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

53.A carnival has a game of chance: a fair coin is tossed. If it lands heads you win $1.00 and if it lands tails you lose $0.50. How much should a ticket to play this game cost if the carnival wants to break even?

A.$0.25

B.$0.50

C.$0.75

D.$1.00

E(X) = (.5) $1 + (.5) (-$.50) = $0.50 - $0.25 = $0.25.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

54.Ephemeral Services Corporation (ESCO) knows that nine other companies besides ESCO are bidding for a $900,000 government contract. Each company has an equal chance of being awarded the contract. If ESCO has already spent $100,000 in developing its bidding proposal, what is its expected net profit?

A.$100,000

B.$90,000

C.-$10,000

D.$0

E(X) = (1/9) $900,000 = $100,000. ESCO only can expect to cover its sunk cost (no profit).

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

55.The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?

A.1.2

B.1.0

C.1.5

D.2.0

For each X, multiply X time P(X) and sum the values.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

56.The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that at least 1 student comes to office hours on any given Monday?

A..30

B..40

C..50

D..60

P(X 1) = 1 - P(X = 0) = 1 - .40 = .60.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

57.The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that fewer than 2 students come to office hours on any given Monday?

A..10

B..40

C..70

D..90

P(X < 2) = P(X = 0) + P(X = 1) = .40 + .30 = .70.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

58.The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?

A.1.1

B.1.3

C.1.7

D.1.9

For each X, multiply X time P(X) and sum the values.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

59.Given the following probability distribution, what is the expected value of the random variable X?

A.175

B.150

C.200

D.205

For each X, multiply X time P(X) and sum the values.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-02 Solve problems using expected value and variance.Topic: Discrete Distributions

60.Which of the following characterizes a Bernoulli process?

A.A random experiment that has only two outcomes.

B.The probability of "success" varies with each trial.

C.Either outcome has the same chance of occurrence.

D.The "success" must be a desirable outcome.

Review characteristics of the Bernoulli process.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Bernoulli Distribution

61.The binomial distribution describes the number of:

A.trials to obtain the first "success" in a Bernoulli process.

B.trials to obtain n "successes" in a Bernoulli process.

C."successes" or "failures" in a Bernoulli process.

D."successes" in n Bernoulli trials.

Review characteristics of the binomial distribution.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

62.Which of the following is not a requirement of a binomial distribution?

A.Constant probability of success

B.Only two possible Bernoulli outcomes

C.Fixed number of trials

D.Equally likely outcomes

Review characteristics of the binomial distribution.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

63.The binomial distribution is symmetrical when:

A. = 1 and 1 - = 0.

B. = and 1 - = .

C. = and 1 - = .

D. = 0 and 1 - = 1.

Review characteristics of the binomial distribution.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

64.The variance will reach a maximum in a binomial distribution when:

A. = 1 and 1 - = 0.

B. = and 1 - = .

C. = and 1 - = .

D. = 0 and 1 - = 1.

Review formula for the binomial distribution standard deviation.

AACSB: AnalyticBlooms: RememberDifficulty: 3 HardLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

65.Which distribution is most strongly right-skewed?

A.Binomial with n = 50, = .70

B.Binomial with n = 50, = .90

C.Binomial with n = 50, = .40

D.Binomial with n = 50, = .10

Review characteristics of the binomial distribution.

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

66.A random variable is binomially distributed with n = 16 and = .40. The expected value and standard deviation of the variables are:

A.2.00 and 1.24

B.4.80 and 4.00

C.6.40 and 1.96

D.2.00 and 1.20

Review characteristics of the binomial distribution.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

67.The expected value (mean) of a binomial variable is 15. The number of trials is 20. The probability of "success" is:

A..25

B..50

C..75

D..30

Set E(X) = n = (20) = 15 and solve for .

AACSB: AnalyticBlooms: UnderstandDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

68.If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

A..6174

B..3826

C..8131

D..1869

Use Appendix A with n = 8 and = .90 to find P(X 7) or else use the Excel function =1-BINOM.DIST(6,8,.90,1) = .8131.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

69.In Quebec, 90 percent of the population subscribes to the Roman Catholic religion. In a random sample of eight Quebecois, find the probability that the sample contains at least five Roman Catholics.

A..0050

B..0331

C..9950

D..9619

Use Appendix A with n = 8 and = .90 to find P(X 5) or else use the Excel function =1-BINOM.DIST(4,8,.90,1) = .99498.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

70.Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?

A..2055

B..2362

C..7946

D..4417

Use Appendix A with n = 12 and = .20 to find P(X 3) or else use the Excel function =1-BINOM.DIST(2,12,.20,1) = .44165.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

71.The probability that a visitor to an animal shelter will adopt a dog is .20. Out of nine visits, what is the probability that at least one dog will be adopted?

A..8658

B..3020

C..5639

D..1342

Use Appendix A with n = 9 and = .20 to find P(X 1) or else use the Excel function =1-BINOM.DIST(0,9,.20,1) = .865778.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

72.Based on experience, 60 percent of the women who request a pregnancy test at a certain clinic are actually pregnant. In a random sample of 12 women, what is the probability that at least 10 are pregnant?

A..0639

B..1424

C..0196

D..0835

Use Appendix A with n = 12 and = .60 to find P(X 10) or else use the Excel function =1-BINOM.DIST(9,12,.60,1) = .08344.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

73.If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

A..5987

B..3151

C..0116

D..1872

Use Appendix A with n = 10 and = .05 find P(X = 0) or else use the Excel function =BINOM.DIST(0,10,.05,0) = .59874.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

74.Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned?

A..9950

B..9619

C..0331

D..1488

Use Appendix A with n = 8 and = .10 to find P(X < 3) or else use the Excel function =BINOM.DIST(2,8,.1,1) = .96191.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

75.The probability that an Oxnard University student is carrying a backpack is .70. If 10 students are observed at random, what is the probability that fewer than 7 will be carrying backpacks?

A..3504

B..2001

C..6177

D..2668

Use Appendix A with n = 10 and = .70 to find P(X < 7) or else use the Excel function =BINOM.DIST(6,10,.7,1) = .35039.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

76.An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

A..5615

B..2775

C..7161

D..0388

Use Appendix A with n = 16 and = .15 to find P(X 2) or else use the Excel function =1-BINOM.DIST(1,16,.15,1) = .7161.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

77.A random variable X is distributed binomially with n = 8 and = 0.70. The standard deviation of the variable X is approximately:

A.0.458

B.2.828

C.1.680

D.1.296

Use the formula for the binomial standard deviation.

AACSB: AnalyticBlooms: UnderstandDifficulty: 1 EasyLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

78.Suppose X is binomially distributed with n = 12 and = .20. The probability that X will be less than or equal to 3 is:

A..5584

B..7946

C..2362

D..7638

Use Appendix A with n = 12 and = .20 to find P(X 3) or else use the Excel function =BINOM.DIST(3,12,.2,1) = .79457.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

79.Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and = .25?

A.=BINOM.DIST(RAND(), 16, .25, 0)

B.=BINOM.DIST(0, 16, .25, RAND())

C.=BINOM.INV(16, .25, RAND())

D.=BINOM.INV(0, 16, .25, RAND())

This is the Excel 2010 function for the inverse of a binomial.

AACSB: TechnologyBlooms: RememberDifficulty: 3 HardLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

80.A network has three independent file servers, each with 90 percent reliability. The probability that the network will be functioning correctly (at least one server is working) at a given time is:

A.99.9 percent.

B.97.2 percent.

C.95.9 percent.

D.72.9 percent.

Use Appendix A with n = 3 and = .90.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

81.Which statement concerning the binomial distribution is correct?

A.Its PDF covers all integer values of X from 0 to n.

B.Its PDF is the same as its CDF when = .50.

C.Its CDF shows the probability of each value of X.

D.Its CDF is skewed right when < .50.

Review definitions of the binomial distribution. The binomial domain is X = 0, 1, ..., n.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-03 Define probability distribution; PDF; and CDF.Topic: Binomial Distribution

82.Historically, 2 percent of the stray dogs in Southfield are unlicensed. On a randomly chosen day, the Southfield city animal control officer picks up seven stray dogs. What is the probability that fewer than two will be unlicensed?

A..8681

B..9921

C..3670

D..0076

Use Appendix A with n = 7 and = .02.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-05 Find binomial probabilities using tables; formulas; or Excel.Topic: Binomial Distribution

83.The domain of X in a Poisson probability distribution is discrete and can include:

A.any real X value.

B.any integer X value.

C.any nonnegative integer X value.

D.any X value except zero.

For a Poisson random variable, X = 0, 1, 2, (no upper limit).

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

84.On Saturday morning, calls arrive at TicketMaster at a rate of 108 calls per hour. What is the probability of fewer than three calls in a randomly chosen minute?

A..1607

B..8913

C..2678

D..7306

Use Appendix B with = 108/60 = 1.8.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

85.On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade.

A..7408

B..1992

C..1494

D..9502

Use Appendix B with = 3.0.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

86.On average, an IRS auditor discovers 4.7 fraudulent income tax returns per day. On a randomly chosen day, what is the probability that she discovers fewer than two?

A..0518

B..0427

C..1005

D..1523

Use Appendix B with = 4.7.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

87.On a Sunday in April, dog bite victims arrive at Carver Memorial Hospital at a historical rate of 0.6 victim per day. On a given Sunday in April, what is the probability that exactly two dog bite victims will arrive?

A..0875

B..0902

C..0988

D..0919

Use Appendix B with = 0.6.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

88.If tubing averages 16 defects per 100 meters, what is the probability of finding exactly 2 defects in a randomly chosen 10-meter piece of tubing?

A..8795

B..2674

C..3422

D..2584

Use Appendix B with = 16/10 = 1.6.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

89.Cars are arriving at a toll booth at a rate of four per minute. What is the probability that exactly eight cars will arrive in the next two minutes?

A.0.0349

B.0.1396

C.0.9666

D.0.0005

Use Appendix B with = 4.0.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

90.Arrival of cars per minute at a toll booth may be characterized by the Poisson distribution if:

A.the arrivals are independent.

B.no more than one arrival can occur in a minute.

C.there is only one lane leading to the booth.

D.the mean arrival rate is at least 30.

Events per unit of time with no clear upper limit.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

91.The coefficient of variation for a Poisson distribution with = 5 is:

A.35.2 percent.

B.58.9 percent.

C.44.7 percent.

D.31.1 percent.

Use the coefficient of variation with standard deviation equal to the square root of the mean.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

92.The coefficient of variation for a Poisson distribution with = 4 is:

A.35.2 percent.

B.58.9 percent.

C.50.0 percent.

D.26.4 percent.

The Poisson standard deviation is the square root of the mean.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-06 Find Poisson probabilities using tables; formulas; or Excel.Topic: Poisson Distribution

93.For which binomial distribution would a Poisson approximation be unacceptable?

A.n = 30, = 0.02

B.n = 50, = 0.03

C.n = 200, = 0.10

D.n = 500, = 0.01

We want n 20 and .05.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

94.For which binomial distribution would a Poisson approximation be acceptable?

A.n = 60, = 0.08

B.n = 100, = 0.15

C.n = 40, = 0.03

D.n = 20, = 0.20

We want n 20 and .05 for an acceptable Poisson approximation.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

95.For which binomial distribution would a Poisson approximation not be acceptable?

A.n = 35, = 0.07

B.n = 95, = 0.01

C.n = 80, = 0.02

D.n = 50, = 0.03

We want n 20 and .05 for an acceptable Poisson approximation.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

96.The true proportion of accounts receivable with some kind of error is .02 for Venal Enterprises. If an auditor randomly samples 200 accounts receivable, what is the approximate Poisson probability that fewer than two will contain errors?

A..1038

B..0916

C..1465

D..0015

Since n 20 and .05 we can set = n = (200)(.02) = 4.0 and use Appendix B to find P(X 1), or else use the Excel cumulative distribution function =POISSON.DIST(1,4.0,1) = .09158.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

97.The probability that a rental car will be stolen is 0.0004. If 3500 cars are rented, what is the approximate Poisson probability that 2 or fewer will be stolen?

A..3452

B..2417

C..5918

D..8335

Since n 20 and .05 we can set = n = (3500)(.0004) = 1.4 and use Appendix B to find P(X 2), or else use the Excel cumulative distribution function =POISSON.DIST(2,1.4,1) = .8335.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

98.The probability that a customer will use a stolen credit card to make a purchase at a certain Target store is 0.003. If 400 purchases are made in a given day, what is the approximate Poisson probability that 4 or fewer will be with stolen cards?

A..0053

B..0076

C..9923

D..0555

Since n 20 and .05 we can set = n = (400)(.003) = 1.2 and use Appendix B, or else use the Excel cumulative distribution function =POISSON.DIST(4,.003*400,1) = .9923.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

99.The probability that a ticket holder will miss a flight is .005. If 180 passengers take the flight, what is the approximate Poisson probability that at least 2 will miss the flight?

A..9372

B..0628

C..1647

D..2275

Since n 20 and .05 we can set = n = (.005)(180) = 0.9 and use Appendix B to find P(X 2), or else use the Excel cumulative distribution function = 1-POISSON.DIST(1,0.9,1) = .2275.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

100.The probability that a certain daily flight's departure from ORD to LAX is delayed is .02. Over six months, this flight departs 180 times. What is the approximate Poisson probability that it will be delayed fewer than 2 times?

A..4471

B..3028

C..1257

D..1771

Since n 20 and .05 we can set = n = (180)(.02) = 3.6 and use Appendix B to find P(X 1) or else use the Excel cumulative distribution function =POISSON.DIST(1,3.6,1) = .12569.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-07 Use the Poisson approximation to the binomial (optional).Topic: Poisson Distribution

101.If X is a discrete uniform random variable ranging from 0 to 12, find P(X 10).

A..1126

B..1666

C..2308

D..2500

3 out of 13 outcomes (don't forget to count 0 as an outcome).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-04 Know the mean and variance of a uniform discrete model.Topic: Uniform Distribution

102.If X is a discrete uniform random variable ranging from one to eight, find P(X < 6).

A..6250

B..5000

C..7500

D..3750

We count five out of eight outcomes that meet this requirement.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-04 Know the mean and variance of a uniform discrete model.Topic: Uniform Distribution

103.If X is a discrete uniform random variable ranging from one to eight, its mean is:

A.4.0

B.4.5

C.5.0

D.5.5

The mean is halfway between the lower and upper limits 1 and 8.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-04 Know the mean and variance of a uniform discrete model.Topic: Uniform Distribution

104.If X is a discrete uniform random variable ranging from 12 to 24, its mean is:

A.18.5.

B.16.0.

C.18.0.

D.19.5.

The mean is halfway between the lower and upper limits 12 and 24.

AACSB: AnalyticBlooms: RememberDifficulty: 1 EasyLearning Objective: 06-04 Know the mean and variance of a uniform discrete model.Topic: Uniform Distribution

105.At Ersatz University, the graduating class of 480 includes 96 guest students from Latvia. A sample of 10 students is selected at random to attend a dinner with the Board of Governors. Use the binomial model to obtain the approximate hypergeometric probability that the sample contains at least three Latvian students.

A..3222

B..1209

C..8791

D..6778

Since n/N < .05 we can use Appendix A with n = 10 and = 96/480 = .20 to find P(X 3).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

106.There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.

A..3087

B..1681

C..3602

D..8319

Since n/N < .05 we can use Appendix A with n = 5 and = 27/90 = .30 to find P(X 1).

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

107.Use the binomial model to find the approximate hypergeometric probability of at least two damaged flash drives in a sample of five taken from a shipment of 150 that contains 30 damaged flash drives.

A.0.9421

B.0.0579

C.0.7373

D.0.2627

Since n/N < .05 we can use Appendix A with n = 5 and = 30/150 = .20 to find P(X 2).

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

108.On a particular day, 112 of 280 passengers on a particular DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding passes. In a random sample of eight passengers, use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

A..2322

B..8263

C..2926

D..5613

Since n/N < .05 we can use Appendix A with n = 8 and = 112/280 = .40 to find P(X = 4).

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

109.A clinic employs nine physicians. Five of the physicians are female. Four patients arrive at once. Assuming the doctors are assigned randomly to patients, what is the probability that all of the assigned physicians are female?

A..0397

B..0295

C..0808

D..0533

You can't use the binomial approximation because we have sampled more than 5% of the population (n/N = 4/9 = .444) so use the hypergeometric formula with x = 4, n = 4, s = 5, N = 9 or use the Excel function =HYPGEOM.DIST(4,4,5,9,0) = .03938.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-08 Find hypergeometric probabilities using Excel.Topic: Hypergeometric Distribution

110.There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs on the third Visa transaction?

A..0192

B..0025

C..0247

D..0200

Use the formulas for the geometric PDF (not the CDF) with = .02 to find P(X = 3) = .02(1 - .02)3-1 = .02(.98)2 = .02(.9604) = .019208.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

111.Ten percent of the corporate managers at Axolotl Industries majored in humanities. What is the probability that the first humanities major is the fifth manager you meet?

A..0656

B..8561

C..5904

D..4095

Use the formulas for the geometric PDF (not the CDF) with = .10 to find P(X = 5) = .10(1 - .10)5-1 = .10(.90)4 = .10(.6561) = .06561.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

112.Ten percent of the corporate managers at Axolotl Industries majored in humanities. What is the expected number of managers to be interviewed until finding the first one with a humanities major?

A.15

B.20

C.10

D.17

The geometric mean is 1/ = 1/(.10) = 10.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

113.When you send out a resume, the probability of being called for an interview is .20. What is the probability that the first interview occurs on the fourth resume that you send out?

A..4096

B..1024

C..2410

D..0016

Use the formulas for the geometric PDF (not the CDF) with = .20 to find P(X = 4) = .20(1 - .20)4-1 = .20(.80)3 = .20(.512) = .1024.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

114.When you send out a resume, the probability of being called for an interview is .20. What is the expected number of resumes you send out until you get the first interview?

A.5

B.7

C.10

D.12

The geometric mean is 1/ = 1/(.20) = 5.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

115.When you send out a resume, the probability of being called for an interview is .20. What is the probability that you get your first interview within the first five resumes that you send out?

A..6723

B..1024

C..2410

D..0016

Use the formulas for the geometric CDF (not the PDF) with = .20 to find P(X 5) = 1 -(1-.20)5 = = 1 - (.80)5 = 1 - .32678 = .67232.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

116.There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs within the first 20 Visa transactions?

A..1362

B..4000

C..3324

D..4538

Use the formulas for the geometric CDF (not the PDF) with = .02 to find P(X 20) = 1 -(1-.02)20 = = 1 - (.98)20 = 1 - .6676 = .3324.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

117.There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the expected number of Visa transactions until the first one is rejected?

A.10

B.20

C.50

D.98

The geometric mean is 1/ = 1/(.02) = 50.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

118.The geometric distribution best describes:

A.the number of successes in a sample of n trials.

B.the number of trials until the first success.

C.the number of events in a given unit of time.

D.the process of sampling without replacement.

Review the definition of geometric distribution.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

119.The CDF for the geometric distribution shows:

A.the probability of success in a random experiment consisting of n independent trials.

B.the probability that the first success will occur within a given number of trials.

C.the probability that no success will be obtained in a given Bernoulli trial.

D.the probability of more than one success in the first n trials.

Review the definition of geometric distribution.

AACSB: AnalyticBlooms: RememberDifficulty: 2 MediumLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

120.If the probability of success is .25, what is the probability of obtaining the first success within the first three trials?

A..4218

B..5781

C..1406

D..2228

Use the formulas for the geometric CDF (not the PDF) with = .25 to find P(X 3) = 1 -(1-.25)3 = 1 - (.75)3 = 1 - .421875 = .578125.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

121.If the probability of success is .30, what is the probability of obtaining the first success within the first five trials?

A..0024

B..8319

C..1681

D..9976

Use the formulas for the geometric CDF (not the PDF) with = .30 to find P(X 5) = 1 -(1-.30)5 = 1 - (.70)5 = 1 - .16807 = .83193.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-09 Calculate geometric probabilities (optional).Topic: Geometric Distribution (Optional)

122.A project has three independent stages that must be completed in sequence. The time to complete each stage is a random variable. The expected times to complete the stages are 1 = 23, 2 = 11, 3 = 17. The expected project completion time is:

A.51.

B.23.

C.40.

D.32.

The means can be summed because the stages are independent.

AACSB: AnalyticBlooms: ApplyDifficulty: 1 EasyLearning Objective: 06-11 Apply rules for transformations of random variables (optional).Topic: Transformations of Random Variables (Optional)

123.A project has 3 independent stages that must be completed in sequence. The time to complete each stage is a random variable. The standard deviations of the completion times for the stages are 1 = 5, 2 = 4, 3 = 6. The standard deviation of the overall project completion time is:

A.8.77

B.15.0

C.14.2

D.9.24

The variances can be summed because the stages are independent (Rule 4). You have to square the standard deviations to get the variances 12 = 25, 22 = 16, 32 = 36, then add them and take the square root of the sum. Be careful - the standard deviations cannot be summed.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-11 Apply rules for transformations of random variables (optional).Topic: Transformations of Random Variables (Optional)

124.A stock portfolio consists of two stocks X and Y. Their daily closing prices are independent random variables with standard deviations X = 2.51 and Y = 5.22. What is the standard deviation of the sum of the closing prices of these two stocks?

A.33.55

B.6.48

C.7.73

D.5.79

The variances can be summed because the stages are independent (Rule 4). You have to square the standard deviations to get the variances X2 = 6.3001 and Y2 = 27.2484, then add them and take the square root of the sum. Be careful - the standard deviations cannot be summed.

AACSB: AnalyticBlooms: ApplyDifficulty: 2 MediumLearning Objective: 06-11 Apply rules for transformations of random variables (optional).Topic: Transformations of Random Variables (Optional)

125.A stock portfolio consists of two stocks X and Y. Their daily closing prices are correlated random variables with variances X2 = 3.51 and Y2 = 5.22, and covariance XY = -1.55. What is the standard deviation of the sum of the closing prices of these two stocks?

A.5.63

B.7.18

C.8.73

D.2.68

Use the formula for the variance of correlated (nonindependent) events. We sum the variances and covariance, and then take the square root: X+Y = [X2 + Y2 + XY ]1/2 = [3.51 + 5.22 - 1.55]1/2 = [7.18]1/2 = 2.67955.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-11 Apply rules for transformations of random variables (optional).Topic: Transformations of Random Variables (Optional)

126.The expected value of a random variable X is 140 and the standard deviation is 14. The standard deviation of the random variable Y = 3X - 10 is:

A.42

B.6.48

C.14

D.32

Use the rule for functions of a random variable (Rule 2) to get Y = 3X = (3)(14) = 42. The constant -10 merely shifts the distribution and has no effect on the standard deviation. The mean of Y is not requested.

AACSB: AnalyticBlooms: ApplyDifficulty: 3 HardLearning Objective: 06-11 Apply rules for transformations of random variables (optional).Topic: Transformations of Random Variables (Optional)

127.The expected value of a random variable X is 10 and the standard deviation is 2. The standard deviation of the random variable Y = 2X - 10 is:

A.2

B.4

C.-10

D.-6

Use the rule for functions of a random variable (Rule 2) to get Y = 2X = (2)(2) = 4. The constant -10 merely shifts the distribution and has no effect on the standard deviation. The mean of Y is not