According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source: Data from The Boston Globe on October 17, 2006.)

a. For a random sample of 100 living Americans, find the mean and standard deviation of the proportion that have blue eyes.

b. In a course you are taking with 100 students, half of the students have blue eyes. Would this have been a surprising result if the sample were a random sample of Americans? Answer by finding how many standard deviations that sample result falls from the mean of the sampling distribution of the proportion of 100 students who have blue eyes.

c. In part b, identify the population distribution, the data distribution, and the sampling distribution of the sample proportion.