## 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

- 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.
- 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.
- 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. - 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