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4. PROBABILITY DISTRIBUTIONS
49
As an example, the graph of the normal curve with mean 20 and standard
deviation 5 and the corresponding standard normal curve follow below.
Characteristics of a Normal Distribution
(1) It is symmetric about its mean µ.
(2) Mean = median = mode = µ.
(3) The total area between the curve and the x-axis is 1, with 50% of the
area on each side of the mean.
(4) The 68–95–99.7 rule says that 68% of the area is within one SD of the
mean, 95% within two, and 99.7% within three.
(5) The graph has a maximum at µ and points of inflection at µ ± .
(6) The normal distribution is completely determined by µ and . µ is often
called a location parameter, while , which determines the peakedness
or flatness of the graph, is called a shape parameter.
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