How do you figure that 0.3 SD = 25 here? Obviously, Daigian HAS to be less than 1 SD away from the mean, since Mean-1 SD encompasses more than the 68% in the 68-95-99.7 rule, yet at the same time, 67.5% of women will be stronger than Daigian. But I don't see any evidence for that number below 1 to be as low as 0.3.

Also, your math is entirely off. If 0.3 SD = 25, then 1 SD is 250.3), which gives the number as 83.33.

On the other hand, if Daigian is about .73 SD from the mean, it works out perfectly. This would mean that 68% of the population is between strength 15.75 and 84.25. 67.5% of the population falls betwen 25 and 100. The bell curve is cut off below 0, and correspondingly above 100, so the rest of the population is all under two SD's from the mean. Remember that the 3 sigma rule doesn't stop there. You can go on until as many SDs as you want, with the probability of finding someone more SDs from the mean becoming increasingly impossible. In actual practice, one never needs to find people further and further from the mean to prove a normal distribution. To disprove normal distribution, you need to find many people occupying levels many SDs away from the mean.

Whether we take 25 to be 0.3SD or .73 SD or any other value below one, the only way it would disprove a normal distribution (and hence a bell curve) is if more people were found at the outer edges rather than at the mean. All people being within one sigma is actually a good indicator of normal distribution.


That is not true at all. The 68% value comes from the probability of finding someone in the range on +/1 1 SD from the mean. And it takes into account an open reference range with no limits. In practice, when you restrict a normal distribution to a reference range (0-100 in this case), nothing says that the probabilities of all values a set SD value from the mean will follow the three sigma rule in the range.

For example, take SAT scores. You can't go below 200 or above 800. You're restricting the range here, and since no one can go above or below these values, the bell curve will obviously not approach 0. The SD is 100, the mean is 500, so by the 3 sigma rule, 99.7% of the population is within 3 sigmas, so between 200 and 800. But obviously, 0.3% of the population is NOT above 800 or below 200!


Nope. You're getting this completely wrong.


It is, actually. If you stop making preposterous assumptions.