Quick Start Company makes 12volt car batteries After many ye

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 44.8 months and a standard deviation of 8.7 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.)
%

(b) If Quick Start does not want to make refunds for more than 5% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?

Solution

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 46.8 months and a standard deviation of 8.9 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.) %

P(x<=36) = P(z<=(36- 46.8)/8.9) = P(z<= -1.2134) = 0.112488

11% of batterries expect to replace.

(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)?

P(z<=?) = 0.12

? = -1.175

x value = -1.175*8.9 + 46.8 = 36.3425

guarantee the batteries 36 months