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


The values 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 of the two-way calculator for the normal probability distribution:
                                screenprint normdis    


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normal distribution calculator






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

PROBABILITY OF EXCEEDANCE
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 graphics in accordance to data in the above screenprint

            cumulative normal distribution               normal density distribution


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