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**IF YOU WANT TO COPY THIS, DO IT BEFORE CLASS STARTS
DEFINITION: Normal distribution and Normal curve
A Normal distribution is described by a Normal density
curve. Any particular Normal distribution is completely
specified by two numbers: its mean μ and standard
deviation σ. The mean of a Normal distribution is at the
center of the symmetric Normal curve. The standard
deviation is the distance from the center to the changeof-curvature points on either side.
We abbreviate the Normal distribution with
mean μ and standard deviation σ as
N(μ, σ).
Normal Distributions
All Normal curves have the same overall shape: symmetric, single-peaked, bellshaped.
Any specific Normal curve is completely described by giving its mean μ and its
standard deviation σ.
DEFINITION: The 68–95–99.7 rule
In the Normal distribution with mean\ μ and standard
deviation σ:
Approximately 68% of the observations fall within σ of the
mean μ.
Approximately 95% of the observations fall within 2σ of μ.
Approximately 99.7% of the observations fall within 3σ of μ.
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