You are considering the purchase of a new car and are weighing the choice between a Ford Fusion Hybrid sedan (which assists a gasoline engine with an electric motor powered via regenerative braking) and the Ford Fusion Non-Hybrid sedan (just a standard gasoline engine). The non-hybrid version costs $23,240 with fuel economy of 21 miles per gallon in city driving and 32 miles per gallon in highway driving. The hybrid version of the car costs $25,990 with fuel economy of 43 miles per gallon in city driving and 41 miles per gallon in highway driving. You plan to keep the car for 10 years. Your annual mileage is uncertain; you only know that each year you will drive between 9,000 and 13,000 miles. Based on your past driving patterns, 60% of your miles are city driving and 40% of your miles are highway driving. The current gasoline price is $2.19 per gallon, but you know that gasoline prices vary unpredictably over time.

Compute the net present value (NPV) of the costs of each vehicle (purchase cost 1 gasoline cost) using a discount rate of 3%. Assume that you pay the entire purchase price of the vehicle immediately (Year 0) and the annual gasoline costs are incurred at the end of each year.

a. On average, what the cost savings of the hybrid vehicle over the non hybrid?

b. Because of your concern about the maintenance needs of the hybrid vehicle, you would need to be assured of significant savings to convince you to purchase the hybrid. What is the probability that the hybrid will result in more than $2,000 in savings over the non-hybrid?