Craps is a casino game that involves betting on the outcome when two dice are rolled and summed. Possible outcomes are the integers 2 through 12. One of the most popular bets is called playing the field, which is where bettors win if the sum of the dice equals 2, 3, 4, 9, 10, 11, or 12. Although the odds are still in favor of the house, the bettor wins even money with probability 16/36=.444. If a bettor continually places bets on the field, then each game of craps is independent of every other game.

d.Use the theoretical probability of winning a game of craps in conjunction with the sample size for the number of games played in each sample to determine the sampling distribution of the sample proportion. Be sure to include the shape, mean, and standard error

e. Compare your answers in part (d) with the histogram in part (a) and the mean and standard deviation in part (d). (i.e. Is the shape of the histogram close to what is expected? Are the mean and standard deviation of the sample means close to the theoretical values in part (d)?)

Here is the histogram

Histogram of Expression 5 4 Frequency T! 2 1 0 0.050 0.060 0.070 0.080 0.090 0.100 Expression Histogram of Expression 5 4 Frequency T! 2 1 0 0.050 0.060 0.070 0.080 0.090 0.100 Expression