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For a normal distribution, the probability density (x) i s e v erywhere positive, so in principle, all real numbers are possible. In reality, the probability that a random va r i a b l e i s f a r a way from the mean is so small that this possibility can be often safely ignored. Usually, a small real number k is picked (e.g., 2 or 3) then, with a probability P0(k) 1 (depending on k), the normally distributed random variable with mean a and standard deviation belongs to the interval a = a ; k a + k ]. The actual error distribution may be non-Gaussian hence, the probability P (k) that a random variable belongs to a di ers from P0(k). It is desirable to select k for which the dependence of P0(k) on the distribution is the smallest possible. Empirically, this dependence is the smallest for k 2 1:5 2:5]. In this paper, we g i v e a theoretical explanation for this empirical result.

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