Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.8 years, and standard deviation of 2.4 years. If 22 items are picked at random, 7% of the time their mean life will be less than how many years? Give your answer to one decimal place.

Answer 1

Solution:

It is given that

Mean=12.8 Years and Standard deviation=2.4 Years

Sample Size,n=22

We have to calculate that,7% of the time their mean life will be less than how many years. It means,

It is known that from Z table, the value of Z at 0.07 probability is =-1.476

That is,

Now,

Thus,7% of the time their mean life will be less than 12.0 years.