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 μ and σ 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.