Amechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 31 comma 000 miles and a standard deviation of 2800 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?

Hence, if the tire wears in less than equal to 27410.4 miles, then the mechanic will replace approximately 10% of the tires.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 31,000

Standard Deviation, σ = 2,800

We are given that the distribution of life expectancy is a bell shaped distribution that is a normal distribution.

Formula:

We have to find the value of x such that the probability is 0.10

P(X<x) = 0.10

Calculation the value from standard normal z table, we have,  

Hence, if the tire wears in less than equal to 27410.4 miles, then the mechanic will replace approximately 10% of the tires.