378 normal - NORMAL DISTRIBUTION History The normal curve...

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NORMAL DISTRIBUTION History The normal curve was developed mathematically in 1733 by DeMoivre as an approximation to the binomial distribution. His paper was not discovered until 1924 by Karl Pearson. Laplace used the normal curve in 1783 to describe the distribution of errors . Subsequently, Gauss used the normal curve to analyze astronomical data in 1809. The normal curve is often called the Gaussian distribution. The term bell-shaped curve is often used in everyday usage. Normal Distribution The normal distribution is the most used statistical distribution. The principal reasons are: 1. Normality arises naturally in many physical, biological, and social measurement situations. 2. Normality is important in statistical inference. Normal Curve Applet The applet below plots the normal curve. Object 1 The displayed curve is called the normal density and is denoted by f(x). The density curve is shown by default, but if it is hidden, it can be made visible by selecting the f(x) radio button in the bottom panel. The normal density is used to compute probabilities. Normal Moments The normal distribution is characterized by two parameters: the mean µ and the standard deviation sigma. The mean is a measure of location or center and the standard deviation is a measure of scale or spread. The mean can be any value between ± infinity and the standard deviation must be positive. Each possible value of µ and sigma define a specific normal distribution and collectively all possible normal distributions define the normal family .
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Any member of the normal family can be displayed by changing µ and sigma in the above applet. This is
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