In a normal distribution, the standard deviation tells us specifically what percentage of scores fall within a given distance of the mean.
About 68% of scores fall within one standard deviation of the mean, about 95% within two, and about 99.7% within three.
Because a normal distribution is symmetrical, the scores outside a range split evenly: of the 32% outside one standard deviation, 16% are above and 16% below.
If you know the mean and standard deviation of a normal distribution, the rule tells you where almost every score falls.
Key terms
normal distribution
A symmetrical, bell-shaped distribution.
empirical rule (68-95-99.7 rule)
In a normal distribution, about 68%, 95%, and 99.7% of scores fall within one, two, and three standard deviations of the mean.
Watch out
AP exam: know the three percentages (68, 95, 99.7) and how many standard deviations each one covers.