Question

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.

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