Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 10.7 years and a standard deviation of 0.9 years.

Find the probability that a randomly selected quartz time piece will have a replacement time less than 8.6 years? P(X < 8.6 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 4.1% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? warranty =

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.

Answer 1

a) µ = 10.7

sd = 0.9

                          

                           = P(Z < -2.333)

                           = 0.0098

b)

or, x = 9.1