Most four-year automobile leases allow up to 60,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follows the normal distribution. The mean is 52,000 miles and the standard deviation is 5,000 miles.
a. What percent of the leases will yield a penalty because of excess mileage?
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 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage?