The distribution of family size in a particular tribal society is skewed to the right, with = 5.2 and o = 3.0. These values are unknown to an anthropologist, who samples families to estimate mean family size. For a random sample of 36 families, she gets a mean of 4.6 and a standard deviation of 3.2. (a) Identify the population distribution. State its mean and standard deviation. (b) Identify the sample data distribution. State its mean and standard deviation. (c) Identify the sampling distribution of y. State its mean and standard error and explain what it describes. (d) Find the probability that her sample mean falls within 0.5 of the population mean. (e) Suppose she takes a random sample of size 100. Find the probability that the sample mean falls within 0.5 of the true mean, and compare the answer to that in (d). (f) Refer to (e). If the sample were truly random, would you be surprised if the anthropologist obtained y = 4.0? Why? (This could well happen if the sample were not random.)