Question

A mechanic sells a brand of automobile tire that has a life expectancy that is normally​ distributed, with a mean life of 34 , 000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that​ don't wear well. How should he word his guarantee if he is willing to replace approximately​ 10% of the​ tires?

Answer 1

Answer:

He should word his statement as "Free replacement for tires that wear before 30875 miles."

Step-by-step explanation:

If he is willing to replace 10% of tires he should find the life of tires that gives an area of 10% in the normal distribution graph.

Now for 10% of area standard normal deviate Z can be obtained from normal distribution table

Using normal distribution table for 10% area we have Z = -1.28

Thus we have $Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}$

Applying given values we get

$X=-1.28\times 2500+34000\\\\X=30875miles$