The distribution of family size in a particular society is skewed to the right, with μ = 10.4 and σ = 6.0.

These values are unknown to an anthropologist, who samples families to estimate mean family size. For a random sample of 40 families, the anthropologist gets a mean of 8.6 and a standard deviation of 5.2.

(a) Identify the population distribution and its mean and standard deviation.

(b) Identify the sample data distribution and its mean and standard deviation.

(c) Identify the sampling distribution of ¯y and its mean and standard error, and explain what it describes.

(d) Find the probability that the anthropologist’s sample mean falls within 0.5 of the population mean.

(e) If the sample were truly random, would you be surprised if the anthropologist obtained ¯y = 3.0?Why? (This could well happen if the sample were not random.)