Originally Posted by

**dbooksta** Sorry, Shakarri, I just restated the problem to make it more clear. In this case I'm looking at range statistics, and their samples have a sort of Gamma-like positive skewness.

The sample mean can't be normal, because samples are concentrated near 0, but can never be negative. I don't know how this breaks the central limit theorem, but obviously there's zero probability of a negative observation.

Here's a real result from 1MM simulations of this range statistic: Mean = 1.8, stdev = .9, skew = .6. If we believe this is normally distributed then that's saying there's a 2.2% chance of the variable being negative.