Suppose that x has a binomial distribution with n = 200 and p = .4.

a. Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x.

b. Make continuity corrections for each of the following, and then use the normal approximation to the binomial to find each probability:

(1) P(x = 80)

(2) P(x ≤ 95)

(3) P(x < 65)

(4) P(x ≥ 100)

(5) P(x > 100)