Normal Probability Density Function
Normal Probability Distributions
Normal Probability Distributions are the most important class of probability distributions. The PDF is a bell-shaped curve. It is symmetric about the mean so mean = median = mode and skewness = 0.
This app lets you adjust the values of the mean (mu) and standard deviation (sigma), which are the two parameters that determine the specific normal distribution. You can display either the PDF or CDF curves simultaneously or independently. Four different types of probabilities can be computed and illustrated as vertical lengths on the CDF curve or as areas between the PDF curve and the x-axis. Inverse probabilities of these four types can also be computed and illustrated.
Checking the Parameters checkbox shows the mean and standard deviation illustrated. Note that the PDF curve has two inflection points at one standard deviation above and below the mean. Notice the symmetry of the curves: reflective symmetry about x = mean for the PDF and 180 degree rotational symmetry about (mean, 0.5) for the CDF).
You can also check the Standard Normal checkbox to see the Standard Normal PDF where mean = 0 and standard deviation = 1. This is the distribution of Z-scores from the more general normal distribution, hence is sometimes called the Z-distribution.