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?

Answer 1

Answer:

16172

Step-by-step explanation:

$\mu = 22000$

$\sigma = 3100$

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

$P(\frac{x-\mu}{\sigma}\leq \frac{x-22000}{3100} )=0.03$

Refer the z table

So, z corresponding to p value 0.03 is -1.88

So, $z=\frac{x-\mu}{\sigma}$

$-1.88=\frac{x-22000}{3100}$

$-1.88 \times 3100=x-22000$

$-5828=x-22000$

$-5828+22000=x$

$16172=x$

Hence the minimum number of miles the manufacturer should guarantee that the tires will last is 16172