[wesnerm2]

You're mistaken about the laws of probability. The normal distribution arises from sums of the same distribution. This is most frequently found in sample averages, which is . More accurately, sample averages follow a student T distribution, which converges to a normal distribution as sample size increases to infinity.

In general, humans do not follow a bell curve for complex traits. For instance, it's common to see bimodal/multimodal distributions when there are major demographic differences in the population such as gender, race, economic class, etc. Standardized tests have bell-curves because they are "normed." Experimental questions are thrown out if they are not correlated very well with the result.

Also based on the Chebyshev's inequality, +2 std dev has a minimum percentile of 75%. +2.5 has a minimum percentile of 84%. +3 has a minimum percentile of 89%. +k has a minimum percentile of 1-(1/k^2)

[bostik]

> In general, humans do not follow a bell curve for complex traits. [...] Also based on the Chebyshev's inequality,...

Thank you, this was very helpful. After some quick searches and http://en.wikipedia.org/wiki/Chebyshev%27s_inequality I now also know where the "off by square root of sample size" rule comes from.

I stand corrected and very happily so.

[yummyfajitas]

Not only that, he seems to be conflating standard deviations with productivity multipliers (I'm not exactly sure how to translate his +2 to productivity, I could be misinterpreting), which is definitely wrong.

[bostik]

Heavens, no. That wasn't the idea, and certainly not my intention. It was merely a numerical standard deviance value, nothing more.

Granted, the people at the high end of the scale are probably more productive when facing more difficult problems but that's all. "How much more" is then an altogether different question. I'm not sure if one could even put a figure on it.