Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12 years, and standard deviation of 0.7 years.The 3% of items with the shortest lifespan will last less than how many years?

Asnwer =  (Give your answer rounded to two decimal places.)

Answer 1

Given that a manufacturer knows that their items have a normally distributed lifespan, with a mean of = 12 years, and a standard deviation of = 0.7 years.

Hence to calculate the maximum limit for the lowest 3% life span we need to calculate the Z score which is computed using the excel formula which is =NORM.S.INV(0.003), thus the Z is computed as:

Z = -2.75

Now based on the Z formula the maximum life span for the lowest 3% is calculated as:

So, 3% of items with the shortest lifespan will last less than 10.06