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 44.695 miles and a standard deviation of 4.201 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 fai1 to meet the guaranteed mileage? (Round your final answer to the nearest mile.)

Explanation / Answer

Mean ( u ) =44695
Standard Deviation ( sd )=4201
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.02
Value of z to the cumulative probability of 0.02 from normal table is 2.0537
P( x-u/ (s.d) > x - 44695/4201) = 0.02
That is, ( x - 44695/4201) = 2.0537
--> x = 2.0537 * 4201+44695 = 53322.7992                  

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