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Chapter 7: Q.7.21 (page 296)

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 5construct a table similar to table 7.2 on page293.(There are 6 possible sample) of size 5

(b) For a random sample of size 5determine the probability that themean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean. interpret your result in terms of percentages.

Short Answer

Expert verified

(a)

(b) The probability that xis within 3 billon of渭is0.8333

Step by step solution

01

Part (a) Step 1: Given Information 

Given in the question that,

we have to construct a table with sample size of 5

02

Part(a) Step 2: Explanation 

The sample mean of size 5:

x炉=鈭�i=15xi5

Thus, the samples of size 5and the corresponding means are obtained as shown in the table below:

03

Part (b) Step 1: Given Information 

Given in the question that,

we have to determine the probability that the mean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean.

04

Part(b) Step 2: Explanation 

We have to find P(渭-3鈮�x炉鈮�渭+3)P(渭-3鈮�x炉鈮�渭+3)

P(渭-3鈮�x炉鈮�渭+3)=P(46.5-3鈮�x炉鈮�46.5+3)

=P(43.5鈮�x炉鈮�49.5)

=56=0.8333

Therefore, the probability that xis within 3billion of渭is0.8333

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Most popular questions from this chapter

Officer Salaries. Refer to Problem 5.

a. Use the answer you obtained in Problem 5(b)and Definition 3.11on page 140 to find the mean of the variable x^Interpret your answer.

b. Can you obtain the mean of the variable ix without doing the calculation in part (a)? Explain your answer.

Women at Work. In the article "Job Mobility and Wage Growth" (Monthly Labor Review. Vol. 128. No. 2, pp. 33-39).

A. Light examined data on employment and answered questions regarding why workers separate from their employers. According to the article, the standard deviation of the length of time that women with one job are employed during the first 8 years of their career is 92 weeks. Length of time employed during the first 8 years of a career is a left-skewed variable. For that variable, do the following tasks.

a. Determine the sampling distribution of the sample mean for simple random samples of 50 women with one job. Explain your reasoning.

b. Obtain the probability that the sampling error made in estimating the mean length of time employed by all women with one job by that of a random sample of 50 such women will be at most 20 weeks.

Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it ?

Refer to Exercise 7.5 on page 295.

a. Use your answers from Exercise 7.5(b) to determine the mean, 渭s, of the variable x炉for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, 渭s, of the variable x炉, using only your answer from Exercise 7.5(a).

Does the sample size have an effect on the mean of all possible sample means? Explain your answer.
See all solutions

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