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Normal Distribution

From the probabilistic point of view a data set of a certain population is merely a collection of values randomly drawn from a common distribution which is not yet known. Such a distribution is characterized by a probability density function (PDF) which is often described by means of parameters. The parameters are used to represent a family of functions having the same general shape, and the introduction of such parameters gave rise to the discipline of statistical modeling.

A normal density function

Assuming the normal density function for a certain population, we can predict the chance that the observation from the population is between and . Having formed the density function , we can obtain such a probability, denoted by , as the area under the curve over the range between and . The calculation of this probability is what is known as ``integration'' in light of calculus, and can be obtained numerically by

In order to compute the probability
or
in the form above,
you must use `` `-Inf`'' or `` `+Inf`''
to indicate or
in appropriate boxes.

Z-score. In particular, is called the standard normal distribution. Suppose that a random variable is normally distributed with . Then is called the z-score, and the distribution of becomes the standard normal distribution . Standard normal distribution table contains the area under the standard normal curve from to . This table can be used to compute the probability involving a normal random variable.