Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Americans and their wealth (to the nearest billion dollars) are as shown in the following table. Consider these six people a population of interest.
________________________________________________Wealth
________________________Person________________($ billions)
Bill Gates (G)..........................72
Warren Buffett (B)....................59
Larry Ellison (E).......................41
Charles Koch (C)......................36
David Koch (D)........................36
Christy Walton (W)....................35
a. Calculate the mean wealth, μ, of the six people.
b. For samples of size 2, construct a table similar to Table 7.2 on page 310. (There are 15 possible samples of size 2.)
c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.
d. For a random sample of size 2, what is the chance that the sample mean will equal the population mean?
e. For a random sample of size 2, determine the probability that the mean wealth of the two people obtained will be within 3 (i.e., $3 billion) of the population mean. Interpret your result in terms of percentages.
Exercises 7.11-7.23 are intended solely to provide concrete illustrations of the sampling distribution of the sample mean. For that reason, the populations considered are unrealistically small. In each exercise, assume that sampling is without replacement.