NORMAL DISTRIBUTION

also called Gaussian Distribution, the distribution function that is the indefinite integral of the normal density function, the graph of which is the typical bell-shaped normal curve. The specific form of the normal density function is a constant, k, times the exponential of the negative quadratic -(x - x0)2/2 s2. The quantity x0 is the mean, or average, of the distribution and also corresponds to the point at which the distribution function is a maximum. The quantity sigma (s) is the standard deviation and characterizes the width of the distribution; the probability is about 68 percent that a given value will be found within the interval x0 - s to x0 + s. The constant, k = 1/s , is called the normalizing coefficient and has the effect that the sum or integral of the distribution over all possible values of x will give a total probability of unity.