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Normal Distributions and
the 68-95-99.7 Rule
and Quiz 2.1 Review
AP Statistics
Properties of The
Normal Curve
density curve
single peaked
bell shaped.
The 68-95-99.7 Rule (Also
called the Empirical Rule)
• In the normal distribution with
mean  and standard deviation
• 68% of the observations fall
of the mean 
• 95% of the observations fall
within 2 of the mean 
• 99.7% of the observations fall
within 3 of the mean 
2.8 page 89 IQ Scores
Scores on the Wechsler Adult intelligence Scale
(WAIS, a standard IQ test”) for the 20 to 34 age group
are approximately normally distributed with =110 and
=25. Use the 68-95-99.7 rule to answer these
• About what percent of
people in this age
group have scores
above 110?
• 50%
• About what percent
have scores above
• 2.5%
• In what range do the
middle 95% of all IQ
scores lie?
• 110  50
Quiz Review
• Know the properties of a density
curve and be able to tell if a given
curve is a density curve (you may
have to use basic rules for area of a
rectangle and area of a triangle)
• Know the properties of a normal
• Know the 68-95-99.7 (Empirical Rule)
and how to apply it.