Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Life test revealed that the mean mileage is 47,900 and the standard deviation of the normally distributed distribution of mileage is 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than
5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer
Announce?

Question

Quizplus · Accepted Answer

To find the guaranteed mileage, we need to find the mileage corresponding to the 5th percentile of a normal distribution with a mean of 47,900 and a standard deviation of 2,050. Using the z-score for the 5th percentile, which is approximately -1.645, the calculation is: 47,900 + (-1.645 * 2,050) = 44,528.

Suppose a Tire Manufacturer Wants to Set a Mileage Guarantee