A tire company has developed a new type of steel-belted radial tire. Extensive t

Question

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 37,000 miles and a standard deviation of 3,887 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?

Explanation / Answer

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

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