# 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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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,

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:

Step 3

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

The time leng...

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