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 indicatesthe population of mileages obtained by all tires of this new type is normally distributed with amean of 40,000 miles and a standard deviation of 4,000 miles. The company wishes to offer aguarantee providing a discount on a new set of tires if the original tires purchased qualify theguarantee mileage. What should the guaranteed mileage be if the tire company desires that nomore than 3 percent of the tires will fail to meet the guaranteed mileage?

Explanation / Answer

given nomore than 3% failure corresponds to a probability equal to 0.97 of tires

By looking within the z-score table this gives a z-score of -1.88.
by formulea
(x - 40000) / 4000 = -1.88

x= (-1.88 * 4000)+40,000=32,480
x = 32480

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