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?

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wifilethbridge wifilethbridge · Answer 1 · 2019-10-23T09:16:05+02:00

Answer:

16172

Step-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 -1.88

So, [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