# normal distribution

normal distribution
a symmetric, bell-shaped probability distribution having the density function where x> is the abscissa, f(x) is the ordinate, e is the base of natural logarithms (2.718), μ is the mean, and σ is the standard deviation. The normal distribution is entirely dependent on μ and σ; it is symmetric about the mean, with both tails extending to infinity; and the mean, the median, and the mode are identical. Roughly speaking, the normal distribution characterizes a random variable that is the sum of a large number of independent random effects. More precisely, it is typically the limiting distribution of a standardized sum of an infinite series of random variables with finite variance, each making a negligible contribution to the total variance (a fact known as the central limit theorem, q.v.). For this reason it is common statistical practice to assume that random sampling distributions of statistical measures are â€œapproximately normalâ€ and apply tests (e.g., t-test, analysis of variance) based on the normal distribution. See illustration. Called also gaussian d.  Normal distribution. The approximate percentage of the area (or frequency) lying under the curve between standard deviations is indicated.

Medical dictionary. 2011.

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