Q:

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?

Accepted Solution

A:
Answer:16172Step-by-step explanation:[tex]\mu = 22000[/tex][tex]\sigma = 3100[/tex]We are given that The tire manufacturer wants to offer a money-back guarantee so that no more than 3% of tires will qualify for a refund.So, P(X≤x)=0.03[tex]P(\frac{x-\mu}{\sigma}\leq \frac{x-22000}{3100} )=0.03[/tex]Refer the z table So, z corresponding to p value 0.03 is -1.88So, [tex]z=\frac{x-\mu}{\sigma}[/tex][tex]-1.88=\frac{x-22000}{3100}[/tex][tex]-1.88 \times 3100=x-22000[/tex][tex]-5828=x-22000[/tex][tex]-5828+22000=x[/tex][tex]16172=x[/tex]Hence the minimum number of miles the manufacturer should guarantee that the tires will last is 16172