Variance question

[AaronBrown]

Under a Normal distribution, you will be more than 10 standard deviations from the mean with probability 1.5 x 10^-23. Since this isn't going to happen, if you think it did, either (a) it isn't a Normal distribution, (b) you computed the mean or standard deviation wrong, or (c) you're psychotic (the chances of being too insane to know you're insane is about 0.001, so any time you claim a probability is smaller than this, you should consider the chance that you're crazy).

No more than 1/100 of the observations can lie beyond 10 standard deviations from the mean, regardless of the distribution. Suppose you have a distribution with 0.99 chance of 0, 0.005 chance of -10 and 0.005 chance of +10. The mean is zero, and the standard deviation is 1. 0.01 of the observations are 10 standard deviations from the mean.