Suppose a car company developed a new steel-belted radial tire to be sold through a national chain of discount tires. Because the tire is a new product, the company believes that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Based on road tests with the tires, suppose the estimated mean, μ, tire mileage is 36500 miles and standard deviation, σ, of 5000 miles. Assume the data collected indicate a normal distribution.
a. What percentage of the tires will last more than 40000 miles?
b. What percentage of the tires will last between 28400 and 51200 miles?
c. Suppose the company is considering a guarantee that will provide a discount on replacement tires if the original tires do not provide the guaranteed mileage. What should the guaranteed mileage be if the company wants no more than 9% of the tires to be eligible for the discount guarantee?