Simulations and Demonstrations: The Normal Distribution

• For a good review of the topics in this chapter, see the Z-distribution demonstration for an animated introduction to the normal distribution

• Use this Z-probability demonstration for an animation of equations to better understand the normal distribution and how it is derived.

• Use the following Interactive Z tables to see how probability works with the Normal distribution.
  You can enter z values or p-values from examples in the text.

  If you took the example IQ test in the Background section, calculate your z-score (remember that IQ is constructed to have a mean of 100 and a standard deviation of 16). Enter your IQ number in the blank and see the resulting probabilities. If your IQ value is not what you thought it should be, remember the IQ test is just a sample, not an 'official' test.

• Use this normal distribution simulation to enter the mean and standard deviation for examples in the text.

  Experiment with this simulation and read the explanation. You can see the graph change as you select the 68, 95, and 99 percent rule.
  Try changing the sliders so you can see the density change as you change the mean and standard deviation.

• The Probability Plots may take some moments to load, but this site is well worth the wait. Use the site to explore the normal distribution.

• We have looked at distributions of single variables. Sometimes it is profitable to explore a joint distribution; a distribution of two variables simultaneously. The following 3-D Normal curve allows you to interact with a 3d simulation of two variables. The third dimension (height) represents the probability density.