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 36,483 miles and a standard deviation of 3,734 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

for bottom 2 percentile ; zscore =-2.0537

therefore  guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage =mean +z*std deviation =36483-2.0537*3734=28814 miles  

(please reply: as for taking value of z to 2 decimal that should be 28828)

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