Question

A mechanic sells a brand of automobile tire that has a life expectancy that is normally? distributed, with a mean life of 27 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?

Answer 1

Solution:

Given that,

mean = = 27,000

standard deviation = = 2800

Using standard normal table,

1P(Z < z) = 10%

P(Z < z) = 0.10

P(Z < - 1.282) = 0.74

z = -1.282

Using z-score formula,

x = z * +

x = -1.282 * 2800 + 27,000

= 23410.4

x = 23410.4