Normal distribution problem

Probability Problem

I have a question on the following problem:

The number of tons of ore produced in a mine every week is a random variable with mean 10 and standard deviation 16. If production is observed for 64 weeks, calculate:

For the mine is closed, the average production during the 64 weeks should be at least 14 tons. What is the probability that the mine be closed?

I did the following:

Calculate the probability that the average is above 14. In this case, use:

$\displaystyle Z = \displaystyle\frac{X - \mu}{\sigma_x} = \displaystyle\frac{\overline{X} - \mu}{\displaystyle\frac{\sigma}{\sqrt[ ]{n}}}$

where, $\displaystyle \overline{X} = 14$Substituting, we find that $\displaystyle z = 2$ With this finds your chance.

is right or wrong?

Thank you very much as always ...

A big welcome