Quick Start Company makes 12-volt car batteries. After many years of product tes

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 44.0 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 7% 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

standard deviation=7.9

a)

z(36)=(36-44)/7.9=-1.013

P(z<-1.013)=0.1556

15.56%

b)

P(Z<=z)=0.07

z=-1.476

x=44-1.476*7.9=32.34

32 months

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