Normal Command

Normal( <Mean>, <Standard Deviation>, <Variable Value> ): Evaluates the function \(\Phi \left(\frac{x- \mu}{\sigma} \right) \) at variable value v, where Φ is the cumulative distribution function of N(0,1) with given mean μ and standard deviation σ.

Normal(2, 0.5, 1) yields 0.02 in the Algebra View and \(\frac{erf(-\sqrt{2})+1}{2}\) in the CAS View.

This syntax returns the probability at a given value, that is the area under the normal distribution curve to the left of the given x-coordinate.

Normal( <Mean>, <Standard Deviation>, <Variable Value>, <Boolean Cumulative> ): If Cumulative = true, evaluates the cumulative distribution function of a normal distribution with given mean and standard deviation at the given variable value, otherwise it evaluates the probability density function of the distribution at variable value.
Normal( <Mean>, <Standard Deviation>, x, <Boolean Cumulative> ): If Cumulative = true, creates the cumulative density function (cdf) of a normal distribution with given mean and standard deviation, otherwise it creates the probability density function (pdf) of the distribution.