From actual road tests with the tires, Hankook Tires estimated that the mean tire mileage is 36,500 miles and that the standard

deviation is 5000 miles. Data is normally distributed.

(i) What percentage of the tires can be expected to last more

than 40,000 miles?

(ii) Assume that Hankook Tires 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 guarantee mileage be if the company wants no

more than 10% of the tires to be eligible for the discount

guarantee?