The 68-95-99.7 rule, also called the empirical rule, states that for a normal distribution, approximately 68%, 95%, and 99.7% of the probability
lies within one, two, and three standard deviations
of the mean, respectively. More precisely, if 
has mean 
and standard deviation 
, then
 |
for 
.
Taking 
,
2, and 3 gives probabilities 
(OEIS A178647),
(OEIS A110894),
and 
(OEIS A270712), respectively. The rule is specific
to the normal distribution; it is not a general
statement about arbitrary probability distributions.
