One More- Need Help Today- Statistics Probability

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.5 years, and standard deviation of 2.4 years.

If 3 items are picked at random, 9% of the time their mean life will be less than how many years?

Give your answer to one decimal place.

Answer 1

Remember that the standard error is the standard deviation / sqrt(n).

In Excel, then, we can solve this using

=NORM.INV(9%,12.5,2.4/SQRT(3))

You get 10.6421953289159, which rounds to 10.6