6/23/2019 chapter 6 exploring statistics we b a ssi g n ...2.33 3.29 2 . –/1 pointsaswesbe9...

6/23/2019 Chapter 6 Exploring Statistics

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Current Score : – / 3 Due : Wednesday, June 26, 2019 11:59 PM EDT

1. –/1 pointsASWESBE9 6.AQ.502a.

Use the applet "Useful zscores of the Normal Distribution" to answer the following questions.

(a) What probability range is associated with

90%

95%

99%

99.9%

(b) What is the zvalue for a onetail (upper) probability of 5%?

1.65

1.96

2.33

3.29

2. –/1 pointsASWESBE9 6.AQ.502b.

Use the applet "Probabilities for the Standard Normal Distribution using Text Boxes (Lower Tail)" to answer the following questions.

(a) What is the zscore for an uppertail probability of 0.10?

−1.96

1.645

1.282

−2.33

(b) What is the probability for the region

0.973

0.893

0.613

0.586

Chapter 6 Exploring Statistics (Homework)

P obability & Data Analysis

WebAssign

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z = ±1.96?

−1.75 ≤ z ≤ 1.5?

https://www.webassign.net/aswsbe13/ExploringStatisticsApplets/06_normal_useful_zscores.html

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https://www.webassign.net/aswsbe13/ExploringStatisticsApplets/06_normal_probabilities_boxes.html

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6/23/2019 Chapter 6 Exploring Statistics

https://www 2/2

3. –/1 pointsASWESBE9 6.AQ.502c.

Use the applet "Standard Normal Probability Ranges" to answer the following questions.

(a) What is the probability for the region

0.6833

0.8413

0.3432

0.1587

(b) What zvalue relates to a lowertail probability of 1%?

2.32

1.96

−1.96

−2.32

−1.00 ≤ z ≤ 1.00?

https://www.webassign.net/aswsbe13/ExploringStatisticsApplets/06_normal_probability_ranges.html

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6/23/2019 Chapter 6.1 Homework


1. –/1 pointsASWESBE9 6.E.002.MI.

The random variable x is known to be uniformly distributed between 10 and 20.

(a) Show the graph of the probability density function.

(b) Compute

(c) Compute

(d) Compute

(e) Compute (Round your answer to two decimal places.)

ℹ ℹ

ℹ ℹ

P(x < 15).

P(13 ≤ x ≤ 15).

E(x).

Var(x).

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2. –/1 pointsASWESBE9 6.E.004.

Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generaterandom numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with thefollowing probability density function.

(a) Graph the probability density function.

(b) What is the probability of generating a random number between 0.35 and 0.85?

(c) What is the probability of generating a random number with a value less than or equal to 0.30?

(d) What is the probability of generating a random number with a value greater than 0.80?

(e) Generate 50 random numbers by entering =RAND() into 50 cells of an Excel worksheet.

f(x) = 1 for 0 ≤ x ≤ 10 elsewhere

ℹ ℹ

ℹ ℹ


4/4

This answer has not been graded yet.

(f) Compute the mean and standard deviation for the random numbers in part (e).



Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid inexcess of $20,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $20,000 and$25,000.

(a) Suppose you bid $21,000. What is the probability that your bid will be accepted?

(b) Suppose you bid $24,000. What is the probability that your bid will be accepted?

(c) What amount should you bid in dollars to maximize the probability that you get the property?

$

(d) Suppose you know someone who is willing to pay you $26,000 for the property.

What is the expected profit in dollars if you bid the amount given in part (c)?

$

Find a bid in dollars which produces a greater expected profit than bidding the amount given in part (c). (If an answer does not exist, enterDNE.)

$

Would you consider bidding less than the amount in part (c)? Why or why not?

Yes. There is a bid which gives a greater expected profit than the bid given in part (c), and thus a higher expected profit is possiblewith a bid smaller than the amount in part (c).

No. The bid which maximizes the expected profit is the amount given in part (c), thus it does not make sense to place a smallerbid.

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Current Score : – / 8 Due : Wednesday, June 26, 2019 11:59 PM EDT


Use the following figure as a guide.

Sketch a normal curve for a random variable x that has a mean of and a standard deviation of Label the horizontal axis withvalues of 80, 90, 100, 110, 120, 130, and 140.

Chapter 6.2 Homework (Homework)

WebAssign


Areas Under the Curve for any Normal Distribution

ℹ

μ = 110 σ = 10.

ℹ ℹ

ℹ ℹ





A random variable is normally distributed with a mean of and a standard deviation of

(a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at threestandard deviations above the mean (in this case at 40 and 100).

Sketch a normal curve for the probability density function. Label the horizontal axis with values of 40, 50, 60, 70, 80, 90, and 100.

(b) What is the probability the random variable will assume a value between 50 and 90? (Round your answer to three decimal places.)

(c) What is the probability the random variable will assume a value between 60 and 80? (Round your answer to three decimal places.)

μ = 70 σ = 10.

Areas Under the Curve for any Normal Distribution

ℹ

ℹ ℹ

ℹ ℹ





You may need to use the appropriate appendix table to answer this question.

Given that z is a standard normal random variable, compute the following probabilities. (Round your answers to four decimal places.)

(a)

(b)

(c)



Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)

(a) The area to the left of z is 0.1841.

(b) The area between −z and z is 0.9030.

(c) The area between −z and z is 0.2128.

(d) The area to the left of z is 0.9949.

(e) The area to the right of z is 0.6179.

P(−1.98 ≤ z ≤ 0.45)

P(0.54 ≤ z ≤ 1.24)

P(−1.55 ≤ z ≤ −1.04)

https://www.webassign.net/aswsbe13/appendix-b.pdf


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Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)

(a) The area to the right of z is 0.08.

(b) The area to the right of z is 0.025.

(c) The area to the right of z is 0.05.

(d) The area to the right of z is 0.10.



The average return for largecap domestic stock funds over three years was 14.4%. Assume the threeyear returns were normally distributedacross funds with a standard deviation of 4.4%.

(a) What is the probability an individual largecap domestic stock fund had a threeyear return of at least 19%? (Round your answer to fourdecimal places.)

(b) What is the probability an individual largecap domestic stock fund had a threeyear return of 10% or less? (Round your answer to fourdecimal places.)

(c) How big does the return have to be to put a domestic stock fund in the top 15% for the threeyear period? (Round your answer to twodecimal places.)

%





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5/5



The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standarddeviation of 10 minutes. Answer the following questions.

(a) What is the probability of completing the exam in one hour or less? (Round your answer to four decimal places.)

(b) What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? (Round your answer tofour decimal places.)

(c) Assume that the class has 90 students and that the examination period is 95 minutes in length. How many students do you expect will beunable to complete the exam in the allotted time? (Round your answer up to the nearest integer.)

students



According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847. Assume that annualhousehold income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.

(a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimalplaces.)

(b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)

(c) What is the probability that a household in Maryland has an annual income between $60,000 and $70,000? (Round your answer to fourdecimal places.)

(d) What is the annual income (in $) of a household in the ninetyfirst percentile of annual household income in Maryland? (Round your answerto the nearest cent.)

$

†


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Current Score : – / 3


You may need to use the appropriate appendix table or technology to answer this question.

A binomial probability distribution has and

(a) What are the mean and standard deviation?

meanstandard deviation

(b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.

No, because np ≥ 5 and n(1 − p) ≥ 5.

Yes, because n ≥ 30.

Yes, because np ≥ 5 and n(1 − p) ≥ 5.

Yes, because np < 5 and n(1 − p) < 5.

No, because np < 5 and n(1 − p) < 5.

(c) What is the probability of exactly 23 successes? Use the normal approximation of the binomial distribution to answer this question. (Roundyour answer to four decimal places.)

(d) What is the probability of 18 to 22 successes? Use the normal approximation of the binomial distribution to answer this question. (Roundyour answer to four decimal places.)

(e) What is the probability of 13 or fewer successes? Use the normal approximation of the binomial distribution to answer this question. (Roundyour answer to four decimal places.)


You may need to use the appropriate appendix table or technology to answer this question.

Although studies continue to show smoking leads to significant health problems, 20% of adults in a country smoke. Consider a group of450 adults, and use the normal approximation of the binomial distribution to answer the questions below.

(a) What is the expected number of adults who smoke?

adults

(b) What is the probability that fewer than 80 smoke? Use the normal approximation of the binomial distribution to answer this question.(Round your answer to four decimal places.)

(c) What is the probability that from 95 to 100 smoke? Use the normal approximation of the binomial distribution to answer this question.(Round your answer to four decimal places.)

(d) What is the probability that 115 or more smoke? Use the normal approximation of the binomial distribution to answer this question. (Roundyour answer to four decimal places.)

Chapter 6.3 Homework (Homework)

Chapter 6.3 Homework

WebAssign


p = 0.20 n = 100.


https://www.webassign.net/tparise/beta/stats/distributionIndex.html




https://www.webassign.net/tparise/beta/stats/distributionIndex.html


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2/2


According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring? Use the binomial distributionprobability function discussed in Section 5.5 to answer this question. (Round your answer to four decimal places.)

(b) For a sample of 140 Americans, what is the probability that at least 90 believe global warming is occurring? Use the normal approximationof the binomial distribution to answer this question. (Round your answer to four decimal places.)

(c) As the number of trials in a binomial distribution application becomes large, what is the advantage of using the normal approximation ofthe binomial distribution to compute probabilities?

As the number of trials becomes large, the normal approximation gives a more accurate answer than the binomial probabilityfunction.

As the number of trials becomes large, the normal approximation simplifies the calculations required to obtain the desiredprobability.

(d) When the number of trials for a binomial distribution application becomes large, would developers of statistical software packages prefer touse the binomial distribution probability function shown in Section 5.5 or the normal approximation of the binomial distribution discussed inSection 6.3? Explain.


†


Chapter 6.4 Homework


Current Score : – / 2


Consider the following exponential probability density function.

(a) Write the formula for

(b) Find (Round your answer to four decimal places.)

(c) Find (Round your answer to four decimal places.)

(d) Find (Round your answer to four decimal places.)

(e) Find (Round your answer to four decimal places.)

WebAssignChapter 6.4 Homework (Homework) Last Saved : n/a Saving... ()

f(x) = e for x ≥ 013

−x/3

P(x ≤ x ).0

P(x ≤ 2).

P(x ≥ 3).

P(x ≤ 4).

P(2 ≤ x ≤ 4).




2/2


The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds.

(a) Sketch this exponential probability distribution.

(b) What is the probability that the arrival time between vehicles is 10 seconds or less? (Round your answer to four decimal places.)

(c) What is the probability that the arrival time between vehicles is 6 seconds or less? (Round your answer to four decimal places.)

(d) What is the probability of 32 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)

ℹ ℹ

ℹ ℹ

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6/23/2019 chapter 6 exploring statistics we b a ssi g n ...2.33 3.29 2 . –/1 pointsaswesbe9...

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