**Universality:** This distribution is a universal distribution because except certain conditione Most in all areas nature of frequency distribution is normal. Sir Francis Galton wrote, ‘I know of barcely anything so to impress the imagination as the wonderful form of cosmic order expressed by whe law of frequency of error.’ WJ Youden a famous statistician, has expressed his admiration of the normal distribution in an artistic fashion (symmetrical) as reproduced below:

THE

NORMAL

LAW OF ERROR

STAND OUT IN THE

EXPERIENCE OF MANKIND

AS ONE OF THE BROADEST

GENERALISATION OF NATURAL

PHILOSOPHY. IT SERVES AS THE

GUIDING INSTRUMENT IN RESEARCHES

IN THE PHYSICAL AND SOCIAL SCIENCES AND

IN MEDICINE AGRICULTURE AND ENGINEERING

IT IS AN INDISPENSABLE TOOL FOR THE ANALYSIS AND THE

INTERPRETATION OF THE BASIC DATA OBTAINED BY

OBSERVATION EXPERIMENT.

**2. Study of Natural Phenomenon:** Almost all natural phenomenon possesses the features of normal distribution, such as height of adults, length of leaves of a tree, etc. Therefore, the normal distribution is widely used in the study of natural phenomenon.

**3.
Approximation to Binomial and Poisson Distribution:** The normal distribution serves as a good approximation to
binomial and Poisson distribution particularly, when the number of observations
increases. It may be mentioned that for large values of n, computation of
probability for discrete distribution becomes difficult and in such cases
normal distribution can be used with great ease and convenience.

**4.
Conformity of Sampling Distribution:** Almost, all
the exact sampling distribution, e.g. students, t-distribution, Fisher’s
Z-distribution, Snedecor’s F-distribution and the chi-square distribution
conform to normal distribution for large degrees of freedom.

**5.
Basis of Small Samples:** The whole
theory of small sample is based on the fundamental assumption that the parent
population from which the samples have been drawn follows normal distribution.

**6.
Statistical Quality Control:** It is very
useful in statistical quality control where the control limits are set by using
this distribution.

**7.
Determination of Limits of Population Values:** The normal distribution is properly stated in the central
limit theorem. According to this theorem, we can estimate the upper and lower
limits within which a value of population would be. For example, within a range
of population, Mean + 3S.D., 99.73% or almost all the items are covered.

**Properties
of Normal Distribution/Curve**

The following are the important properties of normal distribution or normal curve:

**1.
Bell Shaped:** The normal
curve is perfectly symmetrical and bell shaped about mean. This means That if
we fold the curve along its vertical axis at the centre, the two halves would
coincide.

**2.
Continuous Distribution:** Normal
distribution is a distribution of continuous variables. Hence, it is called
continuous probability distribution.

**3.
Equality of Central Values :** In a normal
distribution, all central values are equal, i.e.

Mean = Median= Mode

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