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 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 15% 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

Solution :

Given that ,

mean = = 46.0

standard deviation = = 6.9

a) P(x < 36)

= P[(x - ) / < (36 - 46.0) / 6.9]

= P(z < -1.45)

Using z table,

= 0.0735

The percentage is = 7.35%

b) Using standard normal table,

P(Z < z) = 15%

= P(Z < z ) = 0.15

= P(Z < -1.04 ) = 0.15  

z = -1.04

Using z-score formula,

x = z * +

x = -1.04 * 6.9 + 46.0

x = 38.82

x = 39 months