The Heart Association claims that only 10%

of U.S. adults over 30 years of age meet the minimum requirements established by the President’s Council on Fitness, Sports, and Nutrition. Suppose four adults are randomly selected and each is given the fitness test.

a. Find the probability that none of the four adults passes the test.

b. Find the probability that three of the four adults pass the test.

c. Let x represent the number of the four adults who pass the fitness test. Explain why x is a binomial random variable.

d. Use the answers to parts a and b to derive a formula for p1x2 , the probability distribution of the binomial random variable x .