A manufacturer knows that their items have a normally distri

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12 years, and standard deviation of 0.9 years.

If you randomly purchase one item, what is the probability it will last longer than 11 years?

Solution

Normal Distribution
Mean ( u ) =12
Standard Deviation ( sd )=0.9
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 11) = (11-12)/0.9
= -1/0.9 = -1.1111
= P ( Z >-1.111) From Standard Normal Table
= 0.8667