Random Number Generator - Normal Distribution

The normal distribution is the most commonly used probability distribution in statistics. Many other probability distributions are related to this distribution. As the number of random variables increases, the distribution becomes a bell shaped curve. This curve is called the normal curve or Gaussian curve (in honor of the German mathematician Karl Friedrick Gauss, 1777-1855). The normal distribution is defined with mean and standard deviation.

The following example shows input and output from 3 simulations. Each has the same mean (50) with different standard deviation, 5, 10, and 30 respectively. All three simulations have 50,000 iterations and alpha of 5% (for 1 tail test).

The output shows the estimate of skewness, mean, stand deviation, maximum value, minimum value, lower confidence interval, and upper confidence interval from each of the 3 simulations. The skew levels from each of the simulated distributions are closed to zero. That is because the distributions are normal. Notice that both the maximum values and the minumum values are approximately equal to mean x 4 standard deviations and mean x -4 standard deviations respectively.

The following shows the charts generated from the 3 simulations.