Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.7 years, and standard deviation of 2.5 years. if you randomly purchase one item, what is the probability it will last longer than 8 years?

Answer 1

First let us calculate for the z score using the formula:

z = (x – u) / s

where x = 8, u is the mean = 12.7 years, s is the standard deviation

 

z = (8 – 12.7) / 2.5

z = -1.88

 

From the standard probability tables, the p value at z = -1.88 is:

P = 0.0301 = 3.01%