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What Is so Important About the Normal Distributions-ECO6416

# What Is so Important About the Normal Distributions-ECO6416...

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What Is so Important About the Normal Distributions? The term “normal" possibly arose because of the various attempts made to establish this distribution as the underlying rule governing all continuous variables. These attempts were based on false premises and consequently failed. Nonetheless, the normal distribution rightly occupies a preeminent place in the field of probability. In addition to portraying the distribution of many types of natural and physical phenomena (such as the heights of men, diameters of machined parts, etc.), it also serves as a convenient approximation of many other distributions which are less tractable. Most importantly, it describes the manner in which certain estimators of population characteristics vary from sample to sample and, thereby, serves as the foundation upon which much statistical inference from a random sample to population are made. Normal Distribution (called also Gaussian) curves, which have a bell-shaped appearance (it is sometimes even referred to as the “bell-shaped curves") are very important in statistical analysis. In any normal distribution is observations are distributed symmetrically around the mean, 68% of all values under the curve lie within one standard deviation of the mean and 95% lie within two standard deviations. There are many reasons for their popularity. The following are the most important reasons for its applicability: 1. One reason the normal distribution is important is that a wide variety of naturally occurring random variables such as heights and weights of all creatures are distributed

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What Is so Important About the Normal Distributions-ECO6416...

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