## Normal Distribution

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# Normal Distribution

The binomial and the Poisson distribution described above are the most useful theoretical distributions for discrete variables, i.e., they relate to the occurrence of distinct events. In order to have mathematical distributions suitable for dealing with quantities whose magnitude is continuously variable, a continuous distribution is needed. The normal distribution, also called the normal probability distribution, also called the normal probability distribution, happens to be most useful theoretical distribution for continuous variables. Many statistical data concerning business and economic problems are displayed in the form of normal distribution. In fact normal distribution is the cornerstone of modern statistics.The normal model as the underlying law ruling all continuous random variables – thus the name normal. These efforts failed because of the false premises. The normal model has, nevertheless, become the most important probability model in statistical analysis.

The normal distribution is an approximation to binomial distribution. Whether or not p is equal to q, the binomial distribution tends to the form of the continuous curve and when n becomes large at least for the material part of the range. As a matter of fact, the correspondence between the binomial and curve is surprisingly close even for comparatively low values of n, provided that p and q are fairly near equality. The limiting frequency curve obtained, as n becomes large is called the normal frequency curve or simply the normal curve.

The normal curve is represented in several forms. The following is the basic form relating to the curve with mean µ and standard deviation σ.

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The Normal Distribution

P (x) =

Where µ = mean of the normal random variable X.

σ = standard deviation of the given normal distribution

√2∏ = 2.5066

e = 2.7183

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