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 (Q_{3}-M) = and median and first quartile (M-Q_{1}) are equal.
(Q_{3}-M)=(M-Q_{1})
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.