The normal distribution is a continuous probability distribution that is used to model real-world phenomena like human heights, weights, and intelligence scores. It was first discovered in 1733 by Abraham De Moivre and later applied by Laplace and Gauss. The normal distribution is symmetrical and bell-shaped with the mean, median, and mode being equal. It is defined by its mean and standard deviation and describes many natural phenomena.

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2.  It is mainly used to study the behavior of
continuous random variables like
 height
 Weight
 intelligence of a group of students
 It was first discovered by an English Mathematician
Abraham De Moivre in 1733.
 Later discovered and applied by Laplace and Karl
Gauss.
 That’s why it is also known as GAUSSIAN
Distribution
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3.  The normal distribution is a descriptive model
that describes real world situations.
 It is defined as a continuous frequency distribution
of infinite range (can take any values not just
integers as in the case of binomial and Poisson
distribution).
 This is the most important probability distribution in
statistics and important tool in analysis of
epidemiological data and management science.
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4.  Perfectly symmetrical and bell shaped
 Equality of mean median and mode
X=M=Z
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5.  Asymptotic to the base line
 total area under the normal curve is 1
 The ordinate of the normal curve at the mean is
maximum.
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6.  The mean ordinates divide the whole area under the
curve into two equal parts.
 The quartiles Q1 and Q3 are equidistant from the
median i.e.
Q3 - M = M-Q1
 Quartile deviation is 2/3 times the standard deviation
i.e.;
Q.D=2/3S.D
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7.  Mean deviation is 4/5 times the standard deviation,
i.e.;
M.D=4/5S.D
 The normal curve has two points of inflexion i.e. the
point where the curve change its curvature at X -1
and X + 1 .
X -1 X + 1
O
-1 + 1X
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8.  Normal distribution is a distribution of continuous
variables. therefore it is called continuous
probability distribution.
 The constants of normal distribution is denoted by
the following symbols:
mean= X or μ or m
S.D= variance= ²
Moment coeff. Of skewness=ç=0
Moment coeff. Of kurtosis=ß 2 =3
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9.  It has two main parameters namely mean and std
dev
 Area property
The total area under normal curve is 1.
68.26%
95.45%
99.73%
X-scale
Z-Scale-3 -2 -1 0 1 2 3
X
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