NormDis, two-way calculator model for the normal probability distribution with graphics
  Entirely free download and use of software

                                NormDis is a calculator program using a model application (app) made with Delphi software
                                for the normal probability distribution.

The values of a random variable X may follow a normal probability distribution (NPD).
The applicabe NPD is found from the mean (average) M of the X-values and their standard deviation (SD).

With the NPD one can calculate the cumulative probability (CP) of any reference X-value (Xr) or, reversely, one can find the Xr of any CP.                                    
The CP(Xr) is the probability (P) that an X-value is less than the reference value Xr: CP(Xr) = P(X < Xr).

The probability (P) that X occurs between a lower limit (L) and an upper limit (U) can be found from: P(L < X < U) = CP(U) - CP(L).

The normal distribution is used in the Z - test for significance testing of observations.

                                Screenprint: two-way calculator application for the normal probability distribution
                                screenprint normdis    


normal distribution

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There is no analytical solution to the cumulative normal distribution. The NormDis model program uses Hastings' numerical approximation as described in this Wikipedia article in the section "Numerical approximations for the normal CDF" referring to Zelen & Severo (1964).

The exceedance probability (EP), being the probability that X is greater than Xr equals 1 - CP. Hence, when CP is known, the EP is also known.

here comes an image

            NormDis software graphics in accordance to data in the above screenprint of the z-test calculator for the normal probability distribution

            cumulative normal distribution             The NormDis calculator program uses the cumulative normal
            probability distribution for the z - test
            normal density distribution             The NormDis calculator software uses the normal probability density
            distribution for the z - test