Rules for normally distributed data
In practice, one often assumes that the data are from an approximately normally distributed population. If that assumption is justified, then about 68% of the values are within 1 standard deviation of the mean, about 95% of the values are within two standard deviations and about 99.7% lie within 3 standard deviations. This is known as the "68-95-99.7 rule", or "the empirical rule"
The confidence intervals are as follows:
For normal distributions, the two points of the curve which are one standard deviation from the mean are also the inflection points.