Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 13.7 years and a standard deviation of 0.8 years.

Find the probability that a randomly selected quartz time piece will have a replacement time less than 11.8 years?
P(X < 11.8 years) =

Answer 1

X ~ N ( µ = 13.7 , σ = 0.8 )
P ( X < 11.8 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 11.8 - 13.7 ) / 0.8
Z = -2.375
P ( ( X - µ ) / σ ) < ( 11.8 - 13.7 ) / 0.8 )
P ( X < 11.8 ) = P ( Z < -2.375 )
P ( X < 11.8 ) = 0.0088