THE EMPIRICAL RULE
Notice the curve has two horizontal scales; one measured in meals/day and the other
measured in standard deviations from the mean. The distance 2000 to 2200 is the same as the
distance u to u +2σ A special relationship exists between the area under the normal curve and
the horizontal distance from the mean measured in standard deviations.
This relationship is the sixth characteristic of a normal curve and is commonly referred to as
the Empirical rule.
The rule states that: a) the area under the normal curve from u -a to u + σ is approximately
68% of the total area under the curve. b) the area under the normal curve from u -2σ to u + 2σ
is approximately 95%. c) the area under the normal curve from u -3σ to u + 3σ is
The following diagram illustrates this Empirical rule: