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 46.8 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 11% 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 = = 46.8

standard deviation = = 7.9

a) P(x < 36)

= P[(x - ) / < (36 - 46.8) / 7.9]

= P(z < -1.37)

Using z table,

= 0.0853

The percentage is = 8.53%

b) Using standard normal table,

P(Z < z) = 11%

= P(Z < z ) = 0.11

= P(Z < -1.23 ) = 0.11  

z = -1.23

Using z-score formula,

x = z * +

x = -1.23 * 7.9 + 46.8

x = 37.08

x = 37 months