Refer to Exercise 4.35

(p. 193). where the number of shuttle catastrophes caused by booster failure in n missions was treated as a binomial random variable. Using the binomial distribution and the probability of catastrophe determined by the Air Force's risk assessment study ('I3,), you determined the probability of at least one shuttle catastro~he in 25 missions to be S1.55.

a. Based on the guidelines presented in this section, would it have been advisable to approximate this probability using the normal approximation to the binomial distribution? Explain.

b. Regardless of your answer to part

a, use the normal distribution to approximate the binomial probability.

Comment on the difference between the exact and approximate probabilities.

C. Refer to part

a. Would the normal approximation be advisable if n = 100? If n = 500? If n = 1,000?

d. Approximate the probability that more than 25 catastrophes occur in 1,000 flights, assuming that the probability of a catastrophe in any given flight remains %,.