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 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?
A) 44,528
B) 32,960
C) 49,621
D) 40,922

Question

Quizplus · Accepted Answer

To find the guaranteed mileage, we need to determine the mileage at the 5th percentile of the normal distribution. Using the z-score for the 5th percentile, which is approximately -1.645, we calculate: 47,900 + (-1.645 * 2,050) = 44,528 miles.

Suppose a Tire Manufacturer Wants to Set a Mileage Guarantee