Generating Random Numbers with a Normal Distribution
The common programming languages have functions for generating pseudo-random
numbers, but they are white noise-all numbers have equal probability. To test
statistical programs and to generate data for homework problems, a series of
numbers that are normally distributed would be useful. There may be better ways,
but one that works for me uses the equation for the normal distribution curve.
My program asks for 
and plugs it into the equation as f(x) is calculated.
where
- f(x) = equation of the curve
- x = the intensity of the property, e.g., grade on an exam
- µ = mean value for x
- = the standard deviation
The probability of a range of numbers is
the area of that range divided by the total area. This makes it easy to calculate the
probability of a number. The ordinary pseudo-random number generator proposes a
number, its probability is determined, and the dice are rolled again with the
pseudo-random number generator to see if that probability is reached. If so, the
number is added to the list. If not, another number is tested.