7.48 Example 7.18 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Sociochemosensory and Emotional Functions,” Psychological Science [2009]: 1118–1123). Suppose that instead of three shirts, each participant was asked to choose among four shirts and that the process was repeated five times. Then, assuming that the participant is choosing at random, x  number of correct identifications is a binomial random variable with n  5 and p  1⁄4.

a. What are the possible values of x?

b. For each possible value of x, find the associated probability p(x) and display the possible x values and p(x) values in a table.

c. Construct a probability histogram for the probability x.