Jeff, a sales manager of a car dealership, believes that his sales force sells a car to 35% of the customers who stop by the showroom. He needs the dealership to make 50 sales this month to get a special bonus of $100,000. Approximately 120 customers visit the showroom each month. You may assume that customers entering the dealership are independent of one another.

a) What is the probability that he will make his bonus?

b) What is the probability that he will sell between 40 and 50 cars?

c) Assume that Jeff can choose to either increase the motivation of his sales force so that they increase the probability of a sale to 40%, or to increase the number of people walking into the showroom to 140. Which makes it more likely that Jeff will sell 50 cars?

d) A marketing consultant suggests that she can produce an ad campaign that will increase the number of people walking into the showroom to 140 at a cost of $15,000. Assuming that Jeff is risk-neutral and has the budget, should Jeff accept this offer? (Hint: Jeff stands to make $100,000 if he hits his bonus. The increase in probability of making his bonus can be used to compute the expected value using a probability tree.)

e) What is the maximum amount that Jeff should be willing to pay to increase the number of people entering the showroom to 140 (assuming that he is risk-neutral and perfectly rational)?

f) If 20% of customers are “Big Spenders” who earn the firm a lot of money, what is the probability that Jeff will see at least 1 “Big Spender” in the next 10 customers (not see one that buys, but just see one)?