Google doesn't want to help!
I'm able to calculate z-scores, and we are trying to produce a function that given a z-score gives us a percent of the population in a normal distribution that would be under that z-score. All I can find are references to z-score to percentage tables.
Any pointers?
Is it this z-score (link) you're talking about?
If so, the function you're looking for is called the normal cumulative distribution, also sometimes referred to as the error function (although Wikipedia defines the two slightly differently). How to calculate it depends on what programming environment you're using.
If you're programming in C++, you can do this with the Boost library, which has routines for working with normal distributions. You are looking for the cdf accessor function, which takes a z-score as input and returns the probability you want.