# 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:
http://en.wikipedia.org/wiki/Error_function
http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function

### Author

Carsten Lange
Department of Economics
California State  Polytechnic University, Pomona
clange@cpp.edu