9/20/2010
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The Normal Distribution
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Probability Distributions
• The basis of our inferences from samples
to populations are
probability distributions
– Probability distributions are integral equations
that generate curves when they are plotted
– Think of the distributions as smoothed out
versions of histograms from a continuous
variable that has been sampled repeatedly
over an infinite number of observations
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The Normal Distribution
• The most commonly used probability
distribution in statistics is the
unit normal
distribution
, formed from
zscores
– The unit normal distribution is also known as
the “normal curve” or the “bell curve” or the
“Gaussian curve”
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Carl Gauss
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“Gauss was a prodigious mental calculator. Reputedly, when asked how
he had been able to predict the trajectory of [the dwarf planet] Ceres
with such accuracy he replied, „I used logarithms.‟ The questioner then
wanted to know how he had been able to look up so many numbers
from the tables so quickly. „Look them up?‟ Gauss responded. „Who
needs to look them up? I just calculate them in my head!‟”
More on the Normal Distribution
• It is not a single curve; it is an infinite
number of possible curves represented by
a common equation
• Thus there are a “family” of normal curves,
each defined by unique mean and
variance parameters
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More on the Normal Distribution
• The normal distribution is symmetrical
– Most scores are clustered in the middle, with
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 Spring '10
 Fairchild
 Normal Distribution, unit normal table, Carl Gauss

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