United Medicine, Inc., claims that a drug, Viro, significantly relieves the symptoms of a certain viral infection for 80 percent of all patients. Suppose that this drug is given to eight randomly selected patients who have been diagnosed with the viral infection.

a. Let x equal the number of the eight randomly selected patients whose symptoms are significantly relieved. What distribution describes the random variable x? Explain.

b. Assuming that the company’s claim is correct, find p (x ≤ 3).

c. Suppose that of the eight randomly selected patients, three have had their symptoms significantly relieved by Viro. Based on the probability in part b, would you believe the claim of United Medicine, Inc.? Explain.