Explaination of normal distribution in deep and scholarly study base

I am explaining all of the normal distribution in deep and scholarly study base . Actually this concept is some difficult for commerce students or non math group but learning can learn every thing .

In binomial and possion distribution we can calculate theoritical distribution in discreate series form . But continueous series is also so important . Normal distribution is utilized in calculation of distribution in contineous series .

" Normal distribution is useful to study and analysis of continous series."

This concept is discovered first by An English mathematician De - Moivre in 1754 . From 1777 to 1855 , german mathematician used it in physics . Now currently it in solving business problems.

Freatures or characterstics of Normal distribution

1. Value of n is very large.


2. p and q are very small.


3. If m is very large . It is the limiting case of poisson distribution


4. Graphical presentation

5 .Normal curve is always bell shaped

6. Normal Curve has only one mode

7. Q3 - m = m - Q1

8. mean = median = mode

9. rang = +/- .6745 = 6 X S.D.

10. Quartile deviation = probable erro

11. Curve always on x-axis

12. Probable error = .845 of s.d.

13. Normal curve 's arear actually is the area of total probability area . That is always one and one side of curve is 0.5 and other side of mean is 0.5

14. The area corressponding to z >0 or z <>

15. z = x-m/ standard deviation