Normal Curve Simulation  for  Random Variable

Normal Curve Simulation for a Random Variable

This application calculates probabilities based on the Standardized Normal Distribution Curve and shades the area under the curve accordingly. The user can enter a value for the random variable as a benchmark and choose if s/he is interested in the probabilty that a random outcome will be smaller or greater than the entered value. The user can also enter an intervall for the random variable and the application calculates the probability for a random variable to fall in this intervall. In order to use the Standardized Normal Distribution Curve the application transforms the value(s) for the random variable into z-values based on the mean and standard deviation chosen by the user.

How to use the simulation

  1. Choose if you are interested in the probability that a random outcome is smaller/greater than the chosen value or if you are interested in the probabity that the random outcome falls between the two values.
  2. Enter a value as a benchmark for the random varaible or two values (Random Variable Benchmark 0 and Random Variable Benchmark 1) for a specific interval.
  3. Click the "Update Model" button and the simulation calculates (you should check and understand the meaning of the results)
           a) the z-value(s) as (benchmark-mean)/standardDeviation,    
           b) the probability for a random variable to fall in the chosen interval.
  4. The gray area in the diagram reflects the area where the probabilty is based on.

Model Details

The model calculations are based on Cumulative distribution function for the curve and the Error-Function for the area under the curve. See the following two links for more details:


Carsten Lange
Department of Economics
California State  Polytechnic University, Pomona