Question

A mechanic sells a brand of automobile tire that has a life expectancy that is normally​distributed, with a mean life of 30,000 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?

Tires that wear out by _____________ miles will be replaced free of charge.

Answer 1

solution

Given that,

mean = =30000

standard deviation = =  2500

Using standard normal table,

P(Z < z) = 10%

= P(Z < z) = 0.10

= P(Z < -1.28) = 0.10

z = -1.28 Using standard normal z table,

Using z-score formula  

x= z * +

x= -1.28 * 2500+30000

x= 26800

Tires that wear out by ______26800_______ miles will be replaced free of charge.