Warning: slight pedantry ahead. Specifically what this article is noticing is the law of large numbers [1], that sums or averages are "close" to their mean. Th

Warning: slight pedantry ahead. Specifically what this article is noticing is the law of large numbers [1], that sums or averages are "close" to their mean. The central limit theorem says that sums converge in distribution towards being normally distributed. But convergence in distribution isn't a strong statement about tail behavior, and so shouldn't be used in the sort of argument in the post. [1] http://en.wikipedia.org/wiki/Law_of_large_numbers http://en.wikipedia.org/wiki/Law_of_large_numbers