The 2% of items with the shortest lifespan will last less than how many years?

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.5 years, and standard deviation of 1.6 years.

The 2% of items with the shortest lifespan will last less than how many years?

Give your answer to one decimal place.

Answer 1

You'll get this answer by using the following equation X= mean + Z * stdev

You'll need to look up the Z value in a Cumulative Standard Normal Distribution table by looking for a value as close as possible to 0.0200 (from the 2%) I see a value of 0.0202 at Z = - 2.05

So X = 8.5 + (-2.05 x 1.6) = 5.2 years

OR you can use the invNORM function on a Ti-83/84 calculator invNORM(0.02,8.5,1.6) = 5.2