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1. Normal
Distribution -
Introduction & Properties
SUNDARA B. N.
Assistant
Professor

2. Normal Distribution (1)
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.

3. Normal Distribution (2)
The normal distribution was first discovered by
Abraham de Moivre, a French mathematician he
published an article on Doctrine of Chances in
1733.
Later it was applied in natural and social science by
Laplace in 1777.
The Normal Distribution is also known as
Gaussian distribution in honor of Karl Friedrich

4. Normal (Gaussian) Distribution
Z Score (Standard Score)
Z = X – μ
SD
(X=Observed Mean, μ=Population mean)
Z indicates how many standard deviations away from the mean
the point x lies.
Z score is calculated to 2 decimal places.
Tables
Areas under the standard normal curve

5. Characteristics/Properties of Normal
Distribution
 It has two parameters – mean μ and SD
 Mean = Median = Mode all are equal
 The mean of the distribution can be any numerical value
(Negative, Zero or Positive)
 It is symmetric about mean – (Mirror image)
 SD determines how flat and wide the normal curve is
 The total area under the curve for the ND is 1 (or 100%)
 In a Standard Normal Distribution: The mean (μ ) = 0 and
Standard deviation (σ) =1

6. Characteristics/Properties of Normal
Distribution (2)
 The percentage of values in some commonly
used intervals are:
a) 68.3% of the values of a Normal random variable
are within plus or minus ± one SD of its mean
b) 95.4% of the values of a Normal random variable
are within plus or minus ± two SD of its mean
c) 99.7% of the values of a Normal random variable
are within plus or minus ± three SD of its mean

7. 13.55%
2.15%
0.15%
-3 -2 -1 μ 1 2 3
Diagram of Normal Distribution Curve (z
distribution)
34.15%

8. Application/Uses of ND
 It’s application goes beyond describing
distributions
 It is used by researchers and modelers.
 The major use of normal distribution is the role it
plays in statistical inference.
 The z score along with the t –score, chi-square
and F-statistics is important in hypothesis testing.
 It helps managers/management make decisions.