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?
My answer was 43,528, which was wrong. Can you help me understand this wrong answer? It is a normal distribution, but possibly an upper or lower control unit instead?