Normal Command

Normal[ <Mean>, <Standard Deviation>, x ]

Creates probability density function (pdf) of normal distribution.

Normal[ <Mean>, <Standard Deviation>, x, <Boolean Cumulative> ]

If Cumulative is true, creates cumulative distribution function of normal distribution with mean μ and standard deviation σ, otherwise creates pdf of normal distribution.

Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v> ]

Calculates the function Φ((x – μ) / σ) at v where Φ is the cumulative distribution function for N(0,1) with mean μ and standard deviation σ.

Note: Returns the probability for a given x-coordinate's value (or area under the normal distribution curve to the left of the given x-coordinate).

CAS Syntax

Normal[ <Mean>, <Standard Deviation>, <Variable Value> ]

Calculates the function \Phi \left(\frac{x- \mu}{\sigma} \right) where Φ is the cumulative distribution function for N(0,1) with mean μ and standard deviation σ.

Example:

Normal[2, 0.5, 1] yields \frac{-erf(2/\sqrt{2})+1}{2}.