@Michael Rupert

You didn't specify a standard deviation for your distribution, so I assume it will be 1.

Check this out:

Normal distribution - Wikipedia, the free encyclopedia. The second method listed, based on the central limit theorem, is pretty easy to implement. Note that it gives you values from -6 to +6. You can find various ways to scale that to your needs of [-3, 3]. Note, the more numbers you sum up, the more accurate your distribution will be, so long as you scale it down correctly, to fit your +/-3 range.

Note, I'm not a math expert, so I can't really speak to how scaling that method up/down will affect the overall accuracy/precision of your results, nor how to adapt that to a standard deviation other than 1.