Company XYZ know that replacement times for the quartz time pieces it produces a

Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 12.7 years and a standard deviation of 1.7 years. If the company wants to provide a warranty so that only 4.1% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? warranty = years

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Explanation / Answer

Given, mean = 12.7; standard deviation, s = 1.7 years
P(X < x) = 0.041, formula for z score is (x-mean)/s

P(X < x) = P(Z < (x-12.7)/1.7) = 0.041
For p = 0.041, z = -1.7392 (using excel function "=NORM.S.INV(0.041)")
Therefore, (x-12.7)/1.7 = -1.7392, x = 9.7 years

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