Company XYZ know that replacement times for the DVD players it produces are norm

Question

Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 9.3 years and a standard deviation of 2.5 years.

If the company wants to provide a warranty so that only 3.8% of the DVD players 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

z score corresponding to 3.8% area to its left = -1.774

Hence,

Required time length of the warranty = 9.3 - 1.774(2.5) = 4.9 years

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