Question

Quick Start Company makes a 12-volt car batteries. After manyyears of product testing, the company knows the average life of aQuick Start battery is normally distributed, with mean=45 monthsand a std. deviation = 8 months.

If Quick start guarantees a full refund on any battery that failswithin the 36 month period after purchase, what percentage of itsbatteries will the company expect to replace?

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries (to the nearestmonth)

Answer 1

A normal distribution with μ = 45 and σ= 8

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a) Find    Convert the x-score toz-score and then use the normal distributiontable

˜  0.1292 or 12.92%

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b) The question is asking whatx-score is 10% of the data to the left of.  So, we lookat the normal distribution table and find the closest probabilityto .1000.   The closest is between a z-score of -1.28 and-1.29, so let's use -1.285.

Using the z-conversion formula backwards, we can find x ------------> ------>

Solving the equation for x we get:   x= 34.72  months