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?
A) 44,528
B) 32,960
C) 49,621
D) 40,922

Question

Quizplus · Accepted Answer

To ensure no more than 5% of the tires fall below the guaranteed mileage, we use the Z-score associated with the lower 5% tail of a normal distribution, which is approximately -1.645. The formula to calculate the guaranteed mileage is: Mean - Z * Standard Deviation = 47,900 - 1.645 * 2,050 ≈ 44,528.

Suppose a Tire Manufacturer Wants to Set a Mileage Guarantee