Sales Incentive Problem: Calvin is a salesperson at a car dealership. At the beginning

Chapter 9, Problem 3

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Sales Incentive Problem: Calvin is a salesperson at a car dealership. At the beginning of the year, the dealership wants to sell the previous years car models off the lot to make space for new cars. The dealership manager wants minivans to clear out fastest, then station wagons, and other models last, so she puts together two choices of selling incentives for the sales staff during the first week of the new year. Option A: Receive a $100 bonus for each vehicle sold of the previous years models. Option B: Receive a $2000 bonus for selling four minivans, two station wagons, one hybrid car, and one sedan of the previous years models. Calvin estimates that his probability of selling four minivans is 50%, selling two station wagons is 70%, selling a hybrid car is 80%, and selling a sedan is 90%. a. Calculate the mathematical expectation for Calvins bonus if he chooses Option A and sells the required four minivans, two station wagons, one hybrid car, and one sedan. b. Calculate Calvins probability of being able to sell four minivans, two station wagons, one hybrid car, and one sedan. c. Calculate the mathematical expectation for Calvins bonus if he chooses Option B. d. Based on your answers in parts a-c, which option should he choose?