Kelso Motor Parts produces a car battery with a useful life that has a normal distribution.Average life is 40,000 miles, with a standard deviation of 1500 miles.Suppose the company wants to establish a warranty policy.Any battery not lasting as long as the warranty mileage will be replaced free of charge.What warranty mileage would you suggest to ensure that the company won't have to replace more that 3% of the batteries sold?
A)25,992 miles
B)33, 206 miles
C)37,180 miles
D)40,210 miles
E)43,822 miles

Question

Quizplus · Accepted Answer

To ensure that no more than 3% of batteries are replaced, we need to find the mileage corresponding to the 3rd percentile of the normal distribution. Using the z-score for 3% (approximately -1.88), we calculate: 40,000 + (-1.88 * 1500) = 37,180 miles.

Kelso Motor Parts Produces a Car Battery with a Useful