Many three-year automobile leases allow up to 100 000 km. If the lease goes beyond this amount, a penalty per kilometre is added to the lease cost. Suppose the distribution of kilometres driven on three-year leases follows the normal distribution. The mean is 85 000 km and the standard deviation is 8000 km.
a. What percentage of the leases will yield a penalty because of excess distance travelled?
b. If the automobile company wanted to change the terms of the lease so that 25% of the leases went over the limit, where should the new upper limit be set?
c. One definition of a low-mileage car is one that is three years old and has been driven less than 72 000 km. What is the percentage of cars returned that are considered low-mileage?