Chapter 18, Problem 29E

(a)

To determine

To describe the histogram of waist size.

Explanation of Solution

It is given in the question that a study measured the waist size of $250$ men finding a mean of $36.33$ inches and a standard deviation of these measurements. Thus, the distribution of waist size of $250$ men in Utah is uni-modal and slightly skewed right. A typical waist size is approximately $36$ inches, with a standard deviation of approximately $4$ inches.

(b)

To determine

To explain how these histograms demonstrates what the central limit theorem says about the sampling distribution model for sample means.

Explanation of Solution

It is given in the question that a study measured the waist size of $250$ men finding a mean of $36.33$ inches and a standard deviation of these measurements. Thus, all of the histograms show distributions of sample means centered near $36$ inches. As n gets larger, the histograms approach the normal model in shape and standard deviation decreases. The histograms are already fairly normal by the time the sample size reaches $5$ .