Chapter 7.6, Problem 4P

Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and probability of success p = 0.85.

(a) Is it appropriate to use a normal approximation to this binomial distribution? Why?

(b) Compute $\mu \text{ and }\sigma$ of the approximating normal distribution.

(c) Use a continuity correction factor to convert the statement r< 30 successes to a statement about the corresponding normal variable x.

(d) Estimate $P(r<30)$).

(e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.85 to have fewer than 30 successes? Explain.