The success rate of corneal transplant surgery is 85%. The surgery is performed on six patients. (Adapted from St. Luke's Cataract & Laser Institute)

(a) Construct a binomial distribution.

(b) Graph the binomial distribution using a probability histogram. Then describe its shape.

(c) Find the mean, variance, and standard deviation of the probability distribution and interpret the results.

(d) Find the probability that the surgery is successful for exactly three patients. Is this an unusual event? Explain.

(e) Find the probability that the surgery is successful for fewer than four patients. Is this an unusual event? Explain.