Gestation Periods of Humans. For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days. Suppose that you observe the gestation periods for a sample of nine humans.

a. Theoretically, what are the mean and standard deviation of all possible sample means?

b. Use the technology of your choice to simulate 2000 samples of nine human gestation periods each.

c. Determine the mean of each of the 2000 samples you obtained in part (b).

d. Roughly what would you expect the mean and standard deviation of the 2000 sample means you obtained in part

(c) to be? Explain your answers.

e. Determine the mean and standard deviation of the 2000 sample means you obtained in part (c).

f. Compare your answers in parts

(d) and (e). Why are they different?