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.
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.

Previous exercise

The owners of Aunt Erma’s Restaurant in Boston plan an advertising campaign with the claim that more people prefer the taste of their pizza (which we’ll denote by A) than the current leading fast-food chain selling pizza (which we’ll denote by D). To support their claim, they plan to sample three people in Boston randomly. Each person is asked to taste a slice of pizza A and a slice of pizza D. Subjects are blindfolded so they cannot see the pizza when they taste it, and the order of giving them the two slices is randomized. They are then asked which pizza tastes better. Use a symbol with three letters to represent the responses for each possible sample. For instance, ADD represents a sample in which the first subject sampled preferred pizza A and the second and third subjects preferred pizza D.