Question

Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.2 months and a standard deviation of 7.7 months. (a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace? (Round your answer to two decimal places.)

Answer 1

17.11%

Explanation:

since 43.2 months is the mean, and the standard deviation is 7.7 months

that means if we take the z score:

z=(36-43.2)/7.7

now that we know how many standard deviations you are away from the mean: -0.9351

using the zscore table you can find the proportion, or you can use the calculator if you have one that can do that.

you get 0.1711 which in percentages is 17.11%