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 46.0 months and a standard deviation of 7.9 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 6% 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

Part a

WE are given that the average life of a Quick Start battery in months is normally distributed.

Mean = 46

SD = 7.9

Here, we have to find P(X<36)

Z = (X – mean) / SD

Z = (36 – 46)/ 7.9

Z = -1.26582

P(Z< -1.26582) = 0.102788

(By using z-table)

P(X<36) = 0.102788

Required percentage = 10.28%

Part b

Here, we have to find the value of X for which company does not want to make refunds for more than 6% of its batteries.

X = Mean + Z*SD

Mean = 46

SD = 7.9

For lower 6% probability, critical value of Z by using z-table is given as below:

Z = -1.554774

X = 46 - 1.554774*7.9

X = 33.71729

Required Answer: 34 months