Question

From actual road tests with the tires, Hankook Tires estimated that the mean fire mileage is 36,500 miles and that the standard deviation is 5000 miles. Data is normally distributed. What percentage of the tires can be expected to last more than 40,000 miles? Assume that Hankook Tires is considering a guarantee that will provide a discount on replacement tires if the original tires do not provide the guaranteed mileage. What should the guarantee mileage be if the company wants no more than 10% of the tires to be eligible for the discount guaranfee? UNIVER​

Answer 1

Expert's answer

let x denote the number of tires.

x~N(36500,50002)

z=\frac{x-\mu}{\sigma}

σ

x−μ

a) P(x>40000)

z=\frac {40000-36500}{5000}

5000

40000−36500

=0.7

we check the value of p(z>0.7) from the z tables.

=0.24196

24.2% of the tires can be expected to last more than 40000 miles.

b) P(z<0.1)

the value of \phi ^{-1}(0.1)ϕ

−1

(0.1) =-1.28

z=\frac{x-\mu}{\sigma}z=

σ

x−μ

-1.28=\frac{x-36500}{5000}−1.28=

5000

x−36500

=30100 miles

BRAIN LESS ANSWER IS CORRECT