If you don't need a perfect normal distribution then you can get a very good approximation by choosing several random numbers and adding them together. You can then multiply then add by appropriate constants to get the desired average and variance.

For most purposes, adding a dozen is good enough.

If you want better than that, try installing Math::Random.

DISCLAIMER: I am one dissertation short of a PhD in math. (It is hand-written, needed an income so I never cleaned it up and typed it.) Therefore for all intents and purposes, I am a mathematician. :-)