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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

What is the sampling distribution of a statistic? Why is it important?

Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is \(55.4thousand. Assume a standard deviation of \)9.2thousand. Do the following tasks for the variable "annual salary" of classroom teachers.

a. Determine the sampling distribution of the sample mean for samples of size 64Interpret your answer in terms of the distribution of all possible sample mean salaries for samples of 64classroom teachers.

b. Repeat part (a) for samples of size256

c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.

d. What is the probability that the sampling error made in estimating the population means salary of all classroom teachers by the mean salary of a sample of 64classroom teachers will be at most \(1000?

e. Repeat part (d) for samples of size\)256

Baby Weight. The paper "Are Babies Normal?" by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No, 4. pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard deviation of 581 grams.
a. Identify the population and variable.
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Refer to Fig. 7.6on page 306 .

a. Why are the four graphs in Fig. 7.6(a) all centered at the same place?

b. Why does the spread of the graphs diminish with increasing sample size? How does this result affect the sampling error when you estimate a population mean, 渭by a sample mean, x~ ?

c. Why are the graphs in Fig. 7.6(a) bell shaped?

d. Why do the graphs in Figs. 7.6(b)and (c) become bell shaped as the sample size increases?

Refer to Exercise 7.9 on page 295.

a. Use your answers from Exercise 7.9(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 7.9(a).
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