Susan is a sales representative who has a history of making a successful sale from about 80%

Question:

Susan is a sales representative who has a history of making a successful sale from about 80% 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.

(a) Explain why a negative binomial distribution is appropriate for the random variable n. Write out the formula for P(n) in the context of this application.

(b) Compute P(n = 12), P(n = 13), and P(n = 14).

(d) What is the probability that Susan will need more than 14 contacts to get the bonus?

(e) What are the expected value m and standard deviation s of the random variable n? Interpret these values in the context of this application.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...