Bayesian Statistics - Normal distribution problem

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

On this information what is the probability that the mean component dimension

is at least 10?

Thanks!