Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16.2 years and a standard deviation of 1 years.Find the probability that a randomly selected quartz time piece will have a replacement time less than 13.8 years?P(X < 13.8 years) = __________Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.If the company wants to provide a warranty so that only 2.5% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?warranty =  ________ yearsEnter 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.

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Asked Nov 27, 2019
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Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16.2 years and a standard deviation of 1 years.

Find the probability that a randomly selected quartz time piece will have a replacement time less than 13.8 years?
P(X < 13.8 years) = __________

Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If the company wants to provide a warranty so that only 2.5% 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.

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Step 1

The probability that a randomly selected quartz time piece will have a replacement time less than 13.8 years is,

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X— и 13.8-16.2 P(X<13.8) P 1 =P(Z <-2.4) By using Excel fn =NORM.S.DIST (-2.4, TRUE) =0.0082

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Step 2

Thus, the probability that a randomly selected quartz time piece will have a replacement time less than 13.8 years is 0.0082.

Before calculating the time length of the warranty, find the Z-score corresponding to 2.5% or 0.025 calculated using Excel is shown below:

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for X NORM.S.INV(0.025) A1 A E 1 -1.95996

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Step 3

Thus, the Z-score corresponding to 2.5% is -1.96,

The time leng...

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X - Z = X - 16.2 -1.96 1 X 16.2 1.96 X 14.24 X 14.2

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