Coruscant tire company has just developed a new steel-belted radial tire that will be sold through a national chain of discount stores. Since the tire is a new product, Coruscant managers believe that the mileage guarantee offered with the tire will be an important factor in its marketability. Before finalizing the tire mileage guarantee policy, Coruscant's managers want probability information about the number of miles the tires will last. From actual road tests with the tires, Coruscant's engineering group believes that the tire mileage (that is, number of miles the tire will last) is normally distributed with mean 36,500 miles and standard deviation of 4,000 miles.

a) What is the probability that the tire mileage will exceed 40,000 miles?

b) What is the probability that the tire mileage will be between 30,750 and 38,000 miles?

c) What is the median of the distribution of the tire mileage? What are the 20th and

80th percentiles (quantiles) of the distribution of the tire mileage?

d) Managers are considering offering a guarantee that will provide free replacement of tires if the original tires do not exceed 29,500 miles. If the guarantee policy is adopted, what percent of the tires will be replaced free?

e) Assume that the guarantee policy in (d) is adopted. Given that a tire is eligible for free

replacement, what is the probability that tire will last more than 28,000 miles?