A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 44 months and a standard deviation of 7 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
A)30 months
B)52 months
C)35 months
D)57 months

Question

Quizplus · Accepted Answer

We need to find the length of the full-refund guarantee period so that the company doesn't make refunds for more than 10% of its batteries. Let X be the length of the life of a battery. Then X ~ N(44, 7^2) (normal distribution with mean 44 and standard deviation 7).

Let's find the value of X such that 10% of the batteries fail before that time. We want to find x such that P(X < x) = 0.1. This is equivalent to finding the 10th percentile of the normal distribution. Using a standard normal distribution table, we find that the 10th percentile is -1.28 (approximately).

Using the formula for standardizing a normal variable, we have:

-1.28 = (x - 44)/7
-8.96 = x - 44
x = 35.04

Therefore, the company should guarantee its batteries for 35 months.

The best choice is C.

A Certain Company Makes 12-Volt Car Batteries