Hi all! Anyone know how to do this?!

The dimensions of a component from a long production run vary according to
a N(μ, 1) distribution, and the mean dimension μ varies from production run to
production run according to a N(10, 1/4) distribution. From one production run 12
components are drawn at random and their average dimension is found to be 10$\displaystyle \frac{1}{3}$
On this information what is the probability that the mean component dimension
is at least 10?