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 43.4 months and a standard deviation of 6.9 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.) % (b) If Quick Start does not want to make refunds for more than 14% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)? months

Answer 1

Quick Start battery is normally distributed with

a) The probability that the battery fails within the 36-month period after purchase =

14.17%  of its batteries will the company expect to replace.

b) Let the number of months be A above of which company does not want to make refunds.

The critical Z value corresponding to 14% probability is

months

rounding up to the next integer

the company should guarantee the batteries upto 51 months