Question

QUESTION 5      

The Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire. Tests reveal the mean mileage is 67900 with a standard deviation of 2050 miles and that the distribution of miles follows the normal distribution. They want to set the minimum guarantee mileage so that no more than 4 percent of tires will be replaced. What minimum guaranteed mileage should Layton announce?

Answer 1

Solution:

Given: The Layton Tire and Rubber Company's tire has  the mean mileage is 67900 with a standard deviation of 2050 miles and that the distribution of miles follows the normal distribution.

We have to set the minimum guarantee mileage so that no more than 4 percent of tires will be replaced.

that is find x value such that:

Thus find z value such that:

Look in z  table for Area = 0.0400 or its closest area and find corresponding z value.

Area 0.0401 is closest to 0.0400 and it corresponds to -1.7 and 0.05

that is  z = -1.75

Now use following formula to find x value:

Thus minimum guaranteed mileage should Layton announce is 64312 miles.