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EMPIRICAL RULE
68-95-99.7 RULE
Ch. 6 Day 3
AP Statistics
EQ: What is the empirical rule and why do we
need it?
DENSITY CURVE

Properties
 Total
area under the curve is 1
 It lies on or above the horizontal axis
 It describes the overall pattern of distribution
 Areas under the curve represent proportions of
observations
EMPIRICAL RULE
68% of your data falls within 1 standard
deviation of the mean.
 95% of your data falls within 2 standard
deviations of the mean.
 99.7% of your data falls within 3 standard
deviations of the mean.

STEPS TO FOLLOW
1.
2.
3.
4.
What question are you answering?
Check conditions.
Mechanics(picture clearly labeled)
Conclusion

1.
2.
3.
Assuming the heights of college women are
normally distributed with
mean = 65” and std dev = 2.5”:
What percentage of women are taller than
70 inches?
What proportion of women are shorter than
67.5 inches?
What percentage of women are between
60 and 72.5 inches?
The distribution of SAT Math or Verbal scores
is normally distributed with mean 500 and
standard deviation 100. Suppose you earn a
600 on one part of your SAT. Where do you
stand among all students who took that
test?
What proportion of SAT scores fall between
450 and 600?
Suppose a college says it admits only people with
SAT Verbal test scores among the top 15%.
How high a score does it take to be eligible?
NORMAL PROBABILITY PLOT
If the distribution of data is roughly Normal, the
plot is roughly a diagonal straight line
Deviations from a straight line indicate that the
distribution is not Normal
WHAT CAN GO WRONG?
1.
2.
3.
4.
5.
Don’t use a Normal model when the
distribution is not unimodal and symmetric.
Don’t use the mean and standard deviation
when outliers are present.
Don’t round too soon!
Don’t round your results in the middle of
calculation.
Don’t worry about minor differences in results.
HOMEWORK
P. 129 # 26, 30, 46
Uniform Distribution Worksheet