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 44.8 months and a standard deviation of 9.5 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 14% 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 = = 44.8 months.

standard deviation = = 9.5 months.

a) P(x < 36 ) = P[(x - ) / < ( 36 - 44.8 ) / 9.5 ]

= P(z < -0.93 )

Using z table

= 0.1762

The percentage is = 17.62%

b) Using standard normal table

P(Z < z ) = 14%

P(Z < z ) = 0.14

P(Z < -1.08 ) = 0.14

z = -1.08

Using z-score formula,

x = z * +

x = -1.08 * 9.5 + 44.8

x = 34.54

x = 35 months.