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 47.0 months and a standard deviation of 6.5 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 12% 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

µ = 47

sd = 6.5

a)

                            

                             = P(Z < -1.69)

                             = 0.0455

                             = 4.55%

b)

or, x = 47 - 1.175 * 6.5

or, x = 39.36

or, x = 39 months