7.50 Sampling distribution via the binomial Refer to the previous exercise, in which the proportion of people preferring pizza A is p = 0.5 and a sample of size n = 3 is taken. The sampling distribution of the sample proportion of people preferring pizza A as shown in part b of that exercise can also be derived using the binomial distribution with n = 3 and p = 0.5.

a. A sample proportion of 1/3 corresponds to 1 out of 3 randomly sampled persons preferring pizza A.

Show that this occurs with probability 3/8. (Hint: Use the binomial formula with p = 0.5 and x = 1 person out of n = 3 preferring pizza A.)

b. Find the probabilities for the remaining sample proportions by using the binomial distribution with x = 0, 2, or 3.

c. Find the sampling distribution of the sample proportion when n = 4 people (instead of n = 3) are sampled and draw its graph.