Question: Sports and Leisure Anyone who bets money in a casino is classified as a winner if he or she wins more than he or she loses. Casino operators in Atlantic City, New Jersey, believe the proportion of all players who go home a winner is 0.46. Suppose 75 Atlantic City gamblers are selected at random.
a. Find the sampling distribution of the proportion of gamblers who go home winners.
b. Find the probability that the sample proportion is less than 0.40.
c. Find the probability that the sample proportion is more than 0.45.
d. Find a symmetric interval about the mean (p = 0.46) such that the probability that the sample proportion is in this interval is 0.99.