Question

Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data.

Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation.

When forming your answer to this question give an example of a situation from you own field of interest for which a random variable can serve as a model.

Answer 1

ANSWER::

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real life data are usually noisy in nature and difficult to interpret. So it becomes easy to study the characteristics if it is approximated by a known distribution with known, pre calculated characteristics. Approximations introduces errors but as long as it is bearable, the trade off is worth given that the approximation reduces complexity and makes it possible to get an insight into the data.

Normal is preferred more for modelling data as most of the standard tests are based on normal assumptions. hence the assumption gives a wide range of test to choose from.

One situation where the researcher should not use normal approximation is when the sample is very small and the response is discrete in nature. then normal approximation gives erroneous results.

eg for testing the effectiveness of drugs, the target population can be approximated by normal without introducing much error.

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