Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 9.3 years, and standard deviation of 2.7 years.

If 10 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

Let , , n=10

Now , the sampling distribution of the sample mean is approximately normally distributed with sample mean and sample standard deviation

We have ,

...............(I)

From standard normal distribution table, ...............(II)

From (I) and (II) , we get ,

Therefore ,

If 10 items are picked at random, 7% of the time their mean life will be less than 8.04 years.