How do you take the limit of a binomial to get a Gaussian?

I didn't show it mathematically; rather I showed how it happens with the Mathematica notebook. It's actually a consequence of the Central Limit Theorem: see http://en.wikipedia.org/wiki/Central_limit_theorem. I hope it is plausible-- if you play with the Mathematica notebook, you can see how the binomial distribution starts to look more and more like a Gaussian as $n$ increases.