7.45 The Los Angeles Times (December 13, 1992)

reported that what airline passengers like to do most on long flights is rest or sleep; in a survey of 3697 passengers, almost 80% did so. Suppose that for a particular route the actual percentage is exactly 80%, and consider randomly selecting six passengers. Then x, the number among the selected six who rested or slept, is a binomial random variable with n  6 and p  .8.

a. Calculate p(4), and interpret this probability.

b. Calculate p(6), the probability that all six selected passengers rested or slept.

c. Determine P(x  4).