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The probability density, f(x), or the height of the curve above the x axis (see Figures 4.7 and 4.9) of a Normally distributed random variable x, is given by the expression,

(4.3)

where μ is the mean value of x and σ is the standard deviation of x. Note that for the Normal distribution π, is the mathematical constant 3.14159… and not the parameter of a Binomial distribution.

The probability density simplifies for the Standard Normal distribution, since μ = 0 and σ = 1, then the probability density, f(x), of a Normally distributed random variable x, is

(4.4)