uick Start Company makes 12-volt car batteries. After many years of product test

Question

uick 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 44.6 months and a standard deviation of 7.3 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

Explanation / Answer

Ans:

Given that

mean=44.6

standard deviation=7.3

a)

z=(36-44.6)/7.3

z=-1.178

P(z<=-1.178)=0.1194 or 11.94%

b)

P(Z<=z)=0.11

z=normsinv(0.11)=-1.227

x=44.6-1.227*7.3

x=35.65

x=36 months

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