Question

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 10% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce? a. 44,518 b.45,276 c.49,621 d.40,922

Answer 1

Solution:

Given, X follows Normal distribution with,

   = 47900

= 2050

For bottom 10% data , let x be the required cut-off.

P(X < x) = 0.10

For the standard normal variable z , P(Z < z) = 0.10

Use z table , see where is 0.10 probability and then see the corresponding z value.

P(Z < -1.282) = 0.10

So z = -1.28

Now using z score formula ,

x = + (z * ) = 47900 + (-1.28* 2050) = 45276

Required answer : 45276