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PRINTABLE VERSIONQuiz 5

Question 1

Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to thepoint (0.7, 1). The second goes from (0.7, 1) to (0.9, 2) in the xy-plane. What percent of observations fallbelow 0.10?

a) 0.90

b) 0.45

c) 0.10

d) 1.00

e) 0.05

f) None of the above

Question 2

Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to thepoint (0.7, 1). The second goes from (0.7, 1) to (0.9, 2) in the xy-plane. What percent of observations fallbetween 0.7 and 0.9?

a) 0.20

b) 1.00

c) 0.05

d) 0.30

e) 0.50

f) None of the above

Question 3

Consider a uniform density curve defined from x = 0 to x = 6. What percent of observations fall below 4?

a) 0.67

b) 0.40

c) 0.79

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d) 0.17

e) 0.25

f) None of the above

Question 4

Consider a uniform density curve defined from x = 0 to x = 5. What percent of observations fall between 1and 4?

a) 0.25

b) 0.20

c) 0.72

d) 0.80

e) 0.60

f) None of the above

Question 5

Consider a spinner that, after a spin, will point to a number between zero and 1 with “uniform probability”.Determine the probability: P(1⁄6 ≤ X ≤ 19⁄42).

a) 0.45

b) 1.00

c) 0.71

d) 0.29

e) 0.17

f) None of the above

Question 6

The heights of students in a class are normally distributed with mean 54 inches and standard deviation 6inches. Use the Empirical Rule to determine the interval that contains the middle 99.7% of the heights.

a) [42, 66]

b) [36, 72]

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c) [48, 66]

d) [33, 75]

e) [48, 60]

f) None of the above

Question 7

The length of time needed to complete a certain test is normally distributed with mean 74 minutes andstandard deviation 12 minutes. Find the probability that it will take less than 88 minutes to complete the test.

a) 0.4392

b) 0.8783

c) 0.5608

d) 0.1217

e) 0.5000

f) None of the above

Question 8

If X is normally distributed with a mean of 20 and a standard deviation of 2, find P(20 ≤ X ≤ 22).

a) 0.541

b) 0.641

c) 0.841

d) 0.741

e) 0.341

f) None of the above

Question 9

Suppose that X is normally distributed with a mean of 20 and a standard deviation of 18. What is P(X ≥62.48)?

a) 0.991

b) 0.012

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c) 0.491

d) 0.009

e) 0.014

f) None of the above

Question 10

Suppose that x is normally distributed with a mean of 10 and a standard deviation of 2. What is P(x ≤ 14.90)?

a) 0.493

b) 0.993

c) 0.007

d) 0.496

e) 0.994

f) None of the above

Question 11

Suppose that x is normally distributed with a mean of 50 and a standard deviation of 9. What is P(33.53 ≤ x ≤70.97)?

a) 0.495

b) 0.466

c) 0.490

d) 0.956

e) 0.471

f) None of the above

Question 12

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of74 and a standard deviation of 9. The scores on the calculus final are also approximately normallydistributed, with a mean of 82 and a standard deviation of 14. A student scored 79 on the chemistry final and83 on the calculus final. Relative to the students in each respective class, in which subject did the student dobetter?

a) The student did equally well in each course

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b) Chemistry

c) Calculus

d) There is no basis for comparison

e) None of the above

Question 13

Find a value of c so that P(Z ≤ c) = 0.47.

a) 1.08

b) 0.42

c) -0.08

d) 0.08

e) 0.92

f) None of the above

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PRINTABLE VERSIONQuiz 6

Question 1

Suppose that x is normally distributed with a mean of 50 and a standard deviation of 15. What is P(34.55 ≤ x≤ 72.95)?

a) 0.348

b) 0.785

c) 0.442

d) 0.353

e) 0.437

f) None of the above

Question 2

Find a value of c so that P(Z ≥ c) = 0.43.

a) 0.35

b) 0.18

c) 0.02

d) -0.18

e) 0.82

f) None of the above

Question 3

Suppose that x is normally distributed with a mean of 20 and a standard deviation of 15. What is P(-7.45 ≤ x≤ 54.95)?

a) 0.956

b) 0.490

c) 0.468

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d) 0.495

e) 0.466

f) None of the above

Question 4

The length of time needed to complete a certain test is normally distributed with mean 95 minutes andstandard deviation 10 minutes. Find the probability that it will take between 93 and 98 minutes to completethe test.

a) 0.1972

b) 0.8028

c) 0.5000

d) 0.0986

e) 0.4207

f) None of the above

Question 5

The length of time needed to complete a certain test is normally distributed with mean 74 minutes andstandard deviation 17 minutes. Find the probability that it will take more than 70 minutes to complete thetest.

a) 0.7035

b) 0.5000

c) 0.4070

d) 0.5930

e) 0.2965

f) None of the above

Question 6

Which of the following statements is not true?

a) The sampling distribution of sample mean is approximately normal, mound-shaped, and symmetric forn > 30 or n = 30.

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b) The expected value of the sample mean, X, is always the same as the expected value of X, thedistribution of the population from which the sample was taken.

c) The sampling distribution of the sample mean, X, is always reasonably like the distribution of X, thedistribution from which the sample is taken.

d) The larger the sample size, the better will be the normal approximation to the sampling distribution ofsample mean.

e) The standard deviation of the sampling distribution X of sample mean = σ/√n where σ is the standarddeviation of X.

f) None of the above

Question 7

Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and avariance of 300. Select the pair that is the mean and standard error of x.

a) [65, 2.036]

b) [80, 2.136]

c) [65, 2.436]

d) [65, 2.236]

e) [65, 1.936]

f) None of the above

Question 8

A random sample of 1225 16-ounce cans of fruit nectar is drawn from among all cans produced in a run.Prior experience has shown that the distribution of the contents has a mean of 16 ounces and a standarddeviation of 0.16 ounce. What is the probability that the mean contents of the 1225 sample cans is less than15.992 ounces?

a) 0.070

b) 0.090

c) 0.060

d) 0.080

e) 0.040

f) None of the above

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Question 9

The World Health Organization's (W.H.O.) recommended daily minimum of calories is 2600 per individual.The average number of calories ingested per capita per day for the US is approximately 2460 with a standarddeviation of 500. If we take a random sample of 36 individuals from the US, what is the probability that thesample mean exceeds the W.H.O. minimum?

a) 0.006

b) 0.066

c) 0.026

d) 0.046

e) 0.016

f) None of the above

Question 10

Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with amean of 46 days and a standard deviation of 10.5 days. Find the probability that a simple random sample of49 protozoa will have a mean life expectancy of 47 or more days.

a) 0.7475

b) 0.5379

c) 0.4525

d) 0.2525

e) 0.5050

f) None of the above

Question 11

What effect does increasing the sample size have on a distribution of sample means?

a) It will not make any difference

b) It will have less variation

c) It will have more variation

Question 12

Suppose that a random sample of size 25 is to be selected from a population with mean 44 and standarddeviation 7. What is the approximate probability that X will be within 0.5 of the population mean?

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a) 0.7210

b) 0.0569

c) 0.4790

d) 0.2790

e) 0.5580

f) None of the above

Question 13

Suppose that a random sample of size 25 is to be selected from a population with mean 44 and standarddeviation 7. What is the approximate probability that X will be more than 0.5 away from the populationmean?

a) 0.2790

b) 0.0569

c) 0.4790

d) 0.7210

e) 0.5580

f) None of the above

Question 14

Lloyd's Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 64 boxes is selected atrandom from the production line every hour, and if the average weight is less than 15 ounces, the machine isadjusted to increase the amount of cereal dispensed. If the mean for 1 hour is 1 pound and the standarddeviation is 0.2 pound, what is the probability that the amount dispensed per box will have to be increased?

a) 0.9938

b) 0.3773

c) 0.2062

d) 0.0062

e) 0.0124

f) None of the above

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Question 15

In a large population, 92% of the households have cable tv. A simple random sample of 64 households is tobe contacted and the sample proportion computed. What is the mean and standard deviation of the samplingdistribution of the sample proportions?

a) mean = 0.92, standard deviation = 1.2739

b) mean = 0.92, standard deviation = 0.0012

c) mean = 0.92, standard deviation = 0.0339

d) mean = 58.88, standard deviation = 0.0339

e) mean = 58.88, standard deviation = 0.0012

f) None of the above

Question 16

In a large population, 67% of the households have cable tv. A simple random sample of 256 households is tobe contacted and the sample proportion computed. What is the probability that the sampling distribution ofsample porportions is less than 73%?

a) 0.0206

b) 0.4897

c) 0.9794

d) 0.8796

e) 0.1204

f) None of the above