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 that the proportion of all players who go home a winner is 0.46. Suppose 75 Atlantic City gamblers are selected at random.

[3 marks] Find the sampling distribution of the proportion of gamblers who go home winners.

[2 marks] Find the probability that the sample proportion is less than 0.40.

[2 marks] Find the probability that the sample proportion is more than 0.45.

[3 marks] 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

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