Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Life tests revealed that the mean mileage is 47,900 miles and the standard deviation is 2,050. The manufacturer wants to set the guaranteed mileage so that no more than five percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer set? (assume normality)

Question

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire.  Life tests revealed that the mean mileage is 47,900 miles and the standard deviation is 2,050.  The manufacturer wants to set the guaranteed mileage so that no more than five percent of the tires will have to be replaced.  What guaranteed mileage should the manufacturer set?  (assume normality)

drwls · Answer

The worst 5% of the tires (lowest mileage) will have a Z-score of -1.645. Get that from a normal distribution tabe or calculator, such as

http://www.measuringusability.com/zcalcp.php

Subtract 1.645*2050 from the mean mileage for your answer.

tony · Answer

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