34. The distribution of family size in a particular tribal society is skewed to the right, with = 5.2 and a = 3.0. These values are unknown to an anthropologist, who takes a sample of families in this society in order to estimate mean family size. Let Y denote the sample mean family size she obtains, for a random sample of 36 families.

a) Specify the sampling distribuuon of Y.

b) Find the probability that her sample mean falls within .5 of the true mean

c) Suppose she takes a random sample of size 100. Find the probability that the sample incan falls within 5 of the truc mean, and compare the answer to that obtained in part

b) d) Refer to part e). If the sample were truly random. would you be surprised if the an- thropologist obtained = 4.0? Why? (This could well happen if the sample were not randoni.)