Example 6.27 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 performed five times.
a. If a person can’t identify her roommate by smell and is just picking a shirt at random, then x = number of correct identifications is a binomial random variable with n = 5 and p = ¼.
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 histogram displaying the probability distribution of x.