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 44.4 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.)
%

(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 = = 44.4

standard deviation = = 8.9

a) P(x < 36) = P[(x - ) / < (36 - 44.4) /8.9 ]

= P(z < -0.94)

Using z table,

= 0.1736

The percentage is = 17.36%

b) Using standard normal table,

P(Z < z) = 15%

= P(Z < z) = 0.15  

= P(Z < -1.036) = 0.15

z = -1.036

Using z-score formula,

x = z * +

x = -1.036 * 8.9 + 44.4

x = 35.18

x = 35 months.