Well you probably wouldn't be able to directly prove it since defining a metric for it is nontrivial (and IQ's got its own well known problems as a proxy for intelligence), but a huge chunk of psychological and cognitive traits, and not to mention other biological traits like height or whatever, are normally distributed, so I'd be really surprised if intelligence wasn't. I'm not out to prove it since I'm not writing an article for a journal, but I do think it's incredibly likely for the distribution to be normal.

And, I mean, what are the options? A skewed distribution? I sure hope it's skewed so that there's more intelligent people. Or a multimodal distribution? How would that even happen? Etc. etc.