Solve the problem.
-The life expectancy of a car battery is normally distributed. The average (mean) lifetime is 235 weeks with a standard deviation of 15 weeks. If the company guarantees the battery for 4 years, what percentage of the
Batteries sold would be expected to be returned before the end of the warranty period?
A) 0.0719
B) 0.9281
C) 0.0359
D) 0.9641

Question

Quizplus · Accepted Answer

To calculate the percentage of batteries that would be expected to be returned before the end of the warranty period, we need to find the probability that a battery will fail before reaching 4 years (or 208 weeks).

First, we need to standardize the value of 208 weeks using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

z = (208 - 235) / 15 = -1.8

Now, we need to find the probability of a standard normal distribution being less than -1.8, which we can find using a standard normal distribution table or calculator.

The probability is approximately 0.0359, which means that about 3.59% of batteries would be expected to be returned before the end of the warranty period. Therefore, the best choice is C. First, we need to convert 4 years to weeks: 
4 years = 4 x 52 weeks per year = 208 weeks

Next, we need to find the z-score for the cutoff point where a battery would need to be returned before the end of the warranty period. This is calculated as:

z = (cutoff point - mean) / standard deviation
z = (208 - 235) / 15 
z = -1.8

We look up the percentage of the distribution that falls below this z-score using a standard normal distribution table or calculator. This gives us approximately 0.0359, or 3.59%. Therefore, we would expect approximately 3.59% of the batteries sold to be returned before the end of the warranty period.

The correct answer is C.

Solve the Problem. -The Life Expectancy of a Car Battery Is Normally Distributed