Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed...

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15 years and a standard deviation of 2.3 years. Find the probability that a randomly selected quartz time piece will have a replacement time less than 10.2 years? P(X < 10.2 years) = Enter your answer accurate to 4 decimal places. If the company wants to provide a warranty so that only 1.5% 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.

Homework Answers

Answer #1

a) P(X < 10.2)

= P((X - )/ < (10.2 - )/)

= P(Z < (10.2 - 15)/2.3)

= P(Z < -2.09)

= 0.0183

b) P(X < x) = 0.015

or, P((X - )/ < (x - )/) = 0.015

or, P(Z < (x - 15)/2.3) = 0.015

or, (x - 15)/2.3 = -2.17

or, x = -2.17 * 2.3 + 15

or, x = 10.0

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