Need Help Today- Statistics Probability

Question

No matter what I do I can't get the following question right- please help.

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

z = (sample mean - population mean)/(standard deviation/sqrt(sample size)

Need to find z-value such that P(z < z-value) is 0.09.

From standard normal probability table that z value is -1.34.

population mean is 12.5, population standard deviation is 2.4, sample size is 3.

-1.34 = (sample mean - 12.5)/(2.4/sqrt(3))

solve equation for sample mean.