Refer to the previous two exercises but now suppose the population proportion in Boston preferring pizza A is p = 0.6 instead of p = 0.5. (Then, the eight possible outcomes (AAA, AAD, . . . , DDA, DDD) of a sample of size n = 3 are not equally likely, as in part b of Exercise 7.49)
a. Use the binomial distribution to verify that the sampling distribution of the sample proportion in a sample of size n = 3 is given by

b. When n = 100, what is the mean number of persons that prefer pizza A in a sample of size n = 100?
c. Part b found the mean number (or expected value) of persons preferring pizza A in a sample of size 100. What then is the expected proportion of persons preferring pizza A in a sample of size 100? This is the mean of the sampling distribution of the sample proportion.

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Number Preferring A Proportion Preferring A Probability 0.064 1/3 2/3 0.288 0.432 3 0.216