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