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 44,124 miles and a standard deviation of 4,616 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? (Round your final answer to the nearest mile.)

Explanation / Answer

Solution:

No more than 2% failure corresponds to a probability equal to 0.9800 of tires meeting the requirement. By looking within the z-score table this gives a z-score of - 2.0537.

P(x < k) = 0.02
P(Z < k - 44124/4616) = - 2.0537
k = -2.0537 *4616+44124 = 34644.12

Therefore, the guaranteed mileage should be 34,644 miles

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