Suppose a tire manufacturer wants to set a mileage guarantee

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 47,304 miles and a standard deviation of 2,499 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?

42,604

43,194

43,953

43,616

Solution

Z at .05 is -1.645

-1.645*2,303 + 49,069 = 45,281

Answer: D, 45,281