A 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, the managers believe that the mileage guarantee offered with the tire will be an important factor in its marketability. Based on actual road tests with the tires, the 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 = 4000 miles.

(a) The company is currently using a guarantee policy that provides free replacement of tires if the original tires do not last more than 30,000 miles. What percent of the tires will be replaced free under the policy ?

(b) Given that a tire is eligible for free replacement, what is the probability that tire will last more than 28,000 miles ?

(c) Assumethatweselect10tiresrandomlyfromthenewsteel-belted radial tires developed by the company. What is the probability of observing at least 1 tire eligible for free replacement ?

(d) Assume that the company inspects the cars with the new radial tires. How many inspections will result in no free replacements before one found that needs free replacement?

(e) Assume that company wants to change their gurantee policy so that probability of free replacement is no more than 0.035. How should they change the policy in (a) ?