Answer:
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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.10
P(X<x) = 0.10
[tex]P( X < x) = P( z < \displaystyle\frac{x - 31000}{2800})= 0.10[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z\leq -1.282) = 0.10[/tex]
[tex]\displaystyle\frac{x - 31000}{2800} = -1.282\\\\x = 27410.4[/tex]
Hence, if the tire wears in less than equal to 27410.4 miles, then the mechanic will replace approximately 10% of the tires.
