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

16172

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((x-\mu)/(\sigma)\leq (x-22000)/(3100) )=0.03`

Refer the z table

So, z corresponding to p value 0.03 is -1.88

So,
`z=(x-\mu)/(\sigma)`

`-1.88=(x-22000)/(3100)`

`-1.88 * 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