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Chapter 9: The Normal Probability Distribution
Figure 9-11:
Computed probabilities
to be included
for the Two-sigma rule for the Chest Size
data
Three Sigma Rule:
Approximately 99.7 percent of the data values will lie
within three standard deviations of the mean for any normal distribution.
That is, regardless of the values for the mean and standard deviation of the
normal distribution, the probability that the normal random variable will be
within three standard deviations of the mean is approximately equal to
0.997. This means that approximately 0.3% of the values will lie outside of
three standard deviations of the mean. Thus, if we sample from a normal
population we should expect about one in every three hundred and thirty
three of the values (approximately 0.3%) will lie outside three standard
deviations from the mean. Equivalently, we should expect about three
hundred and thirty two out of every three hundred and thirty three values
(approximately 99.7%) will lie within three standard deviations of the mean.
The three sigma rule is illustrated in
Figure 9-12
.