SOLUTION: Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 11 years and a standard deviation of 2 years. Find the pro

Question 1153503: Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 11 years and a standard deviation of 2 years.
Find the probability that a randomly selected quartz time piece will have a replacement time less than 6 years?
P(X < 6 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 0.9% 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.

please help
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
<(6-11)/2 OR <-2.50 and that probability is 0.0062
z-value for 0.009 is -2.366
-2.366*2=x-mean
x=mean-4.732
=11-4.732, or 6.268
round to 6.3 years
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