Superstitions survey. A Harris (Feb. 2013) poll found that one-third of Americans (33%) believe finding and picking up a penny is good luck. Assume that the true proportion of all Americans who believe finding and picking up a penny is good luck is p = .33. In a random sample of 1,000 Americans, let pn represent the proportion who believe finding and picking up a penny is good luck.

a. Describe the properties of the sampling distribution of pn .

b. Find P1pn 6 .402. Interpret this result.

c. Find P1pn 7 .302. Interpret this result.