Normal Distribution

Meaning: According  to ya Lun Chou  There perfectly smooth and symmetrical  curve, resulting  from the expansion of the binomial (p+q)ⁿ   when n approaches infinity  is known  as the  normal curve. Thus  the normal curve may be considered as the limit  towards  which  the binomial distribution approaches as n increases  to infinity. Alternatively  we may say that the normal curve  represents a continuous and infinite  binomial distribution, or simply a normal distribution .

Normal distribution  is a continuous  probability  distribution. During 18^th  century  karl friedrich  gauss  contributed an important role in the development  of normal distribution . so  in his honour this distribution  is often  referred  to as the Gaussian  distribution .This distribution  is also called as normal law  of error  because  gauss  derived its  equation from the stuty  of error in repeated    measurements  of the same.

When n the number  of trails  is very  large or infinite (n-&) and neither p nor q is very small or nearer to equal then binomial distribution  tends  to be a normal distributions.

Properties of Normal Curve

1.      Shape: It is perfectly  symmetrical and bell shaped.

2.      Position of mean, mode and median: Mean ,mode  and median remains  equal  in normal distribution ,they  are found  in the  mid of the distribution , and distribute the area  of curve in   equally two parts.

3.      Asymptotic : As the distance of the curve  from the mean increases, the curve  comes  closer and  closer to the axis  but never  touches it.

4.       Unimodal :  It  has only  one mode  so it sis unimodal.

5.          Continuous Distribution: It is a distribution of continuous  variables.

6.       Equidistance  of Quartiles: The  difference  between third  quartile & median  (Q₃-M) = and median  and first   quartile (M-Q₁) are  equal.

(Q₃-M)=(M-Q₁)

7.      Quartile Deviation and Probable Error: Quartile  deviation is equal to probable  error,  which  is about 2/3  of standard  deviation (QD=0.6745)

8.      Mean Deviation: The mean  deviation about  mean is 4/5 of 0.7979

9.      Points of Inflection ; The  points where the curveity  of normal   curve  changes  its direction  are termed as points  of Inflection.