Computational Aspects of Normal Distribution
•H.P.Gautam
The purpose of this article is not to explain any more the usefulness of normal distribution in decision-making process no matter whether in social sciences or in natural sciences. Nor is the purpose of making any discussions on the theory of how it can be derived. The only objective of writing this article is to acquaint the enthusiastic readers (specially students) with the simple procedure ( iterative procedure) for finding the numerical value of a normally distributed variable. The procedure is simple in the sense that the students even from non-mathematical background can easily use the technique discussed below to find the value, and it will not an exaggeration to say that he or she after going through the article not only can compute an individual value but also can generate the whole table for such values. At most he require a scientific calculator.
It should be bone in mind that a person using normal distribution as an analytical tool need not be familiar with the computational aspect of normal distribution as various computer package and statistical tables are available in the market. However, he must know how the distribution helps him take the right decisions. Though one need not compute the numerical values himself rather than to how to use and interpret these values, yet he will have a deeper understanding how normal distribution works, if he becomes familiar with the computational process too. In this context, the whole discussion is divided into 3 sections. The first section begins with analysis of function of the distribution, while the second one deals with the general procedure for computational technique. Lastly, in the third section a practical example will be solved to justify what we have told in the first and second section of the article. In addition, a computer program will be listed which gives the result up to the correct 4 decimal places
Section-1 Normal distribution function
The equation of normal curve is
The purpose of this article is not to explain any more the usefulness of normal distribution in decision-making process no matter whether in social sciences or in natural sciences. Nor is the purpose of making any discussions on the theory of how it can be derived. The only objective of writing this article is to acquaint the enthusiastic readers (specially students) with the simple procedure ( iterative procedure) for finding the numerical value of a normally distributed variable. The procedure is simple in the sense that the students even from non-mathematical background can easily use the technique discussed below to find the value, and it will not an exaggeration to say that he or she after going through the article not only can compute an individual value but also can generate the whole table for such values. At most he require a scientific calculator.
It should be bone in mind that a person using normal distribution as an analytical tool need not be familiar with the computational aspect of normal distribution as various computer package and statistical tables are available in the market. However, he must know how the distribution helps him take the right decisions. Though one need not compute the numerical values himself rather than to how to use and interpret these values, yet he will have a deeper understanding how normal distribution works, if he becomes familiar with the computational process too. In this context, the whole discussion is divided into 3 sections. The first section begins with analysis of function of the distribution, while the second one deals with the general procedure for computational technique. Lastly, in the third section a practical example will be solved to justify what we have told in the first and second section of the article. In addition, a computer program will be listed which gives the result up to the correct 4 decimal places
Section-1 Normal distribution function
The equation of normal curve is