7. Exercise 6.30 METHODS AND APPLICATIONS A tire company has developed a new typ

Question

7. Exercise 6.30 METHODS AND APPLICATIONS 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 providinga 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? (Use a z-score to 2 decimal places in your intermediate calculations. Round your final answer to the nearest mile.)

Explanation / Answer

7) mean = 44124

standard deviation = 4616

as the distribution is normal therefore the

z score = (x-mean)/standard deviation

we have been given the probability this time and we need to find the k

p(x<=k) = 0.02

we need to find the z score for 0.02 from the z table which comes out to be = -2.05

therefore the k = mean + zscore*standard deviation

k = 44124 - (2.05)*4616 = 34661.2

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