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Slide 1

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Normal Distribution
A random variable X having a probability
density function given by the formula
is said to have a Normal Distribution with
parameters and 2.
Symbolically, X ~ N(, 2).…read more

Slide 2

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Properties of Normal Distribution
1. The curve extends indefinitely to the left and to
the right, approaching the x-axis as x increases in
magnitude, i.e. as x ±, f(x) 0.
2. The mode occurs at x=.
3. The curve is symmetric about a vertical axis
through the mean
4. The total area under the curve and above the
horizontal axis is equal to 1.
i.e.…read more

Slide 3

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Empirical Rule (Golden Rule)
The following diagram illustrates relevant areas
and associated probabilities of the Normal
Distribution. Approximate 68.3% of the area lies
within ±, 95.5% of the area lies within ±2,
and 99.7% of the area lies within ±3.…read more

Slide 4

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For normal curves with the same , they are
identical in shapes but the means are centered
at different positions along the horizontal axis.…read more

Slide 5

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For normal curves with the same mean , the
curves are centered at exactly the same position
on the horizontal axis, but with different standard
deviations , the curves are in different shapes, i.
e. the curve with the larger standard deviation is
lower and spreads out farther, and the curve with
lower standard deviation and the dispersion is
smaller.…read more

Slide 6

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Normal Table
If the random variable X ~ N(, 2), then we can
transform all the values of X to the standardized
values Z with the mean 0 and variance 1, i.e. Z ~
N(0, 1), on letting…read more

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