A tire company has developed a new type of steelbelted radia

A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 39,531 miles and a standard deviation of 4,075 miles. The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased do not exceed the mileage stated in the guarantee. What should the guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage?

Solution

P(X<c)=0.02

--> P((X-mean)/s <(c-43959)/3900)=0.02

--> P(Z<(c-43959)/3900)=0.02

--> (c-43959)/3900= -2.05 (from standard normal table)

So c= 43959-2.05*3900=35964