Waist size revisited Researchers measured the waist sizes of 250 men in a study on body fat. The true mean and standard deviation of the waist sizes for the 250 men are 36.33 inches and 4.019 inches, respectively. In Exercise 41, you looked at the histograms of simulations that drew samples of sizes 2, 5, 10, and 20 (with replacement). The summary statistics for these simulations were as follows:

n mean st. dev. 2 36.314 2.855 5 36.314 1.805 10 36.341 1.276 20 36.339 0.895

a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes?

b) How close are the theoretical values to what was observed in the simulation?

c) Looking at the histograms in Exercise 39, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?

d) What about the shape of the distribution of waist size explains your choice of sample size in part c)?