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)