Are Americans superstitious? A Harris (Feb. 2013) poll of over 2,000 adult Americans was designed to answer this question. One survey item concerned the phrase "see a penny, pick it up, all day long you'll have good luck." The poll found that just one-third of Americans (33%) believe finding and picking up a penny is good luck. Consider a random sample of 20 U.S. adults and let x represent the number who believe finding and picking up a penny is good luck.

a. For this experiment, define the event that represents a "success."

b. Explain why x is (approximately) a binomial random variable.

c. Give the value of p for this binomial experiment.

d. Find P (x < 10).

e. Find P (x = 17).

f. Find P (x > 5).