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 
, 
, and 
, respectively. The rule is specific to the normal
distribution; it is not a general statement about arbitrary probability
distributions.
