5.72.* For a random sample of n subjects, explain why it is about 95% likely that the sample proportion has error no more than 1/

√

n in estimating the population proportion.

(Hint: To show this “1/

√

n rule,” find two standard errors when π = 0.50, and explain how this compares to two standard errors at other values of π.) Using this result, show that n = 1/M2 is a safe sample size for estimating a proportion to within M with 95% confidence.