How to find the probability?

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.5 years, and standard deviation of 3.1 years.

If you randomly purchase one item, what is the probability it will last longer than 8 years?

Answer 1

Compute the z-score:

 

z = (x-μ)/σ

 

where:

• x is the data point = 8 years
• μ is the mean of the data set = 14.5 years
• σ is the standard deviation of the data set = 3.1 years

 

Then look up the probability on a z score table (http://www.z-table.com/).  This is the probability that the item will last less than 8 years.  The probability that it will last more than 8 years is 1 - the probability from the z-score table.