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Chapter 7: Q.7.2 (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 4construct a table similar to table 7.2 on page293.(There are 15 possible sample of size 4

(b) For a random sample of size 4determine 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) Sample size of 4and corresponding means are obtained.

(b) There is 26.67%chance that the mean wealth of the four people will be within 3billion of the population mean.

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 of4

02

Part(a) Step 2: Explanation

The sample mean of size 4:

x炉=鈭�i=14xi4

Thus, the samples of size 4and the corresponding means are obtained as shown in the table below:

Thus Sample size of 4and corresponding means are obtained.

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(46.5-3鈮�x炉鈮�46.5+3)

=P(43.5鈮�x炉鈮�49.5)

=415=0.2667

Therefore, the probability that xis within 3billion of渭is0.2667

Interpretation:

There is 26.67%chance that the mean wealth of the four people will be within 3billion of the population mean.

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Most popular questions from this chapter

NBA Champs Repeat parts (b) and (c) of Exercise 7.41 for samples of size 5. For part (b), use your answer to Exercise 7.15(b).

What is another name for the standard deviation of the variable x ? What is the reason for that name?

Population data: 3,4,7,8

Part (a): Find the mean, 渭, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

Refer to Exercise 7.10 on page 295.

a. Use your answers from Exercise 7.10(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 7.10a).

A variable of a population is normally distributed with mean 渭and standard deviation 蟽. For samples of size n, fill in the blanks. Justify your answers.

a. Approximately 68%of all possible samples have means that lie within of the population mean, 渭

b. Approximately 95%of all possible samples have means that lie within of the population mean, 渭

c. Approximately 99.7%of all possible samples have means that lie within of the population mean, 渭

d. 100(1-伪)%of all possible samples have means that lie within _of the population mean, 渭(Hint: Draw a graph for the distribution of x, and determine the z-scores dividing the area under the normal curve into a middle 1-伪area and two outside areas of伪/2
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