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 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 8% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)

Answer 1

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Normal distribution params are given here:
Mean = 44.8
Stdev = 6.9

a. %age of battery that will replaced by Quick Start: P(X<36) = P(Z< (36-44.8)/6.9) = 0.1011 or 10.11%
b. If Quick Start doesn't want to make refunds for more than 8% then ,let gauraentee be given for c months

So, P(X<=c) = .08
(c-44.8)/6.9 = -1.4051
c = 6.9*-1.4051+44.8
= 35.105 or 35 months

So, the company should guarantee the batteries for atmost 35 months