Question : What is the probability that the mean of a sample is within a certain range (z scores)?

I was helping someone with statistics homework, and the problems primarily focused on normal distribution and z-scores. That was easy enough. I can practically do z-scores in my sleep.

But, I was thrown off by an additional question.  I was used to questions giving me mu and sigma while asking for the percentage of the population being < or > x. Then, I was asked, that in a sample of size n, what is the probability that the mean of the sample being < or > x.  I'm sure I learned this, but somehow it eluded me.  I'm thinking it involves dividing by the square root of n, but I'm not 100% on that.  

I'd like to read up on this (possibly online). Or, if someone has a basic explanation, I'd like to hear it. I obviously have some cobwebs in my head to blow out.

Answer : What is the probability that the mean of a sample is within a certain range (z scores)?

the standard deviation of the mean is proportional to 1/sqrt(n)