I think you're being downvoted a bit unfairly. What most non-statisticians don't realize is that some of the most "unnormal" distributions actually look pretty normally distributed, and some of the most ugly looking distributions actually behave like a normal distribution. When you look at a distribution's pdf, you're only looking at the "center" of the distribution. But what statisticians (usually) care about are the tails of a distribution.

Consider the following example: The [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution) is a pathological example of a distribution with very heavy tails. Heavier than the power law distributions meantioned in the GP. So heavy, the distribution doesn't even have a mean value. But if you just look at the pdf, it looks almost exactly like a gaussian.