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 45 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)?

Question

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 45 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)?
The choice of answers:
58 months
53 months
36 months
45 months
49 months

*I came out with 45 but was told that was wrong. What did I do wrong. Thanks to those who answer in advance.

PsyDAG · Answer

45 months = mean! In a normal distribution, mean = median, 50% are above and are below the mean. How did you "come out with 45"?

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find Z score related to that proportion.

Z = 1.28

Z = (score-mean)/SD

1.28 = (score-45)/7

Solve the above equation.