Susan is a sales representative who has a history of making a successful sale from about 86% of her sales contacts. If she makes 12 successful sales this week, Susan will get a bonus. Let n be a random variable representing the number of contacts needed for Susan to get the 12th sale. Required:
a. Explain why a negative binomial distribution is appropriate for the random variable n.
b. Compute P(n = 12), P(n = 13), and P(n = 14).
c. What is the probability that Susan will need from 12 to 14 contacts to get the bonus?
d. What is the probability that Susan will need more than 14 contacts to get the bonus?
e. What are the expected value μ and standard deviation σ of the random variable n?