Question

The lifetime in miles for a certain brand of tire is normally distributed with a mean of 22,000 miles and a standard deviation of 3,100 miles The tire manufacturer wants to offer a money-back guarantee so that no more than 3% of tires will qualify for a refund. What is the minimum number of miles the manufacturer should guarantee that the tires will last?

a. 15,800 miles
b. 16,170 miles
c. 25,007 miles
d. 27,828 miles

Answer 1

Explanation:

3% = 0.03

we are looking for the 3rd percentile of Z.

checking the Z-table we find as the entry closest to 0.03 to be 0.0301 at z = -1.8 and 0.8.

so, the 3rd percentile of Z is -1.88

the cutoff number (the number of miles, where max. 3% of the tires will qualify for a refund) is

mean value + Z× standard deviation

22000 + -1.88 × 3100 = 16,172 ≈ 16,170

so, b. is correct