Learn by Doing – Normal Random Variables

Published: February 8th, 2013

Category: Activity 1: Learn By Doing, Activity 3: Simulations and Tools

The purpose of this interactive activity is to:

  • Get a better feel for the behavior of normal random variables.
  • Check the accuracy of the Standard Deviation Rule.
  • Do some other calculations for the normal distribution that are beyond what the Standard Deviation Rule can help us with.

As we’ve seen, the Standard Deviation Rule for normal random variables is very useful. The following applet will help you see how accurate the rule is, and do some other calculations for normal distributions that cannot be done using that rule and that will further enhance your understanding of the normal distribution.


  • Drag the flags across each other to get the area between the points.
  • Do not change the settings of the mean and standard deviation in the applet.
  • The numbers on the horizontal axis represent the number of SD (standard deviations) above or below the mean. So, 0 is the mean, +1 is one SD above the mean, -1 is one SD below the mean, etc.



  • Now drag the flags back across each other to find the probabilities in the tails (above and below 1, 2, and 3 standard deviations from the mean). Recall that we mentioned that according to the Standard Deviation Rule, these tails have probabilities 0.16, 0.025 and 0.0015, corresponding to 1, 2 and 3 standard deviations from the mean). Try it.

Recall from the EDA section the quartiles Q1 and Q3. In the context of random variables, Q1 is the value such that P(X < Q1) = 0.25. In other words, the random variable has a 25% chance of having a value that is below Q1. Similarly, Q3 is the value such that P(X < Q3) = 0.75. In other words, the random variable has a 75% chance of having a value below Q3. Another way to think about the quartiles is that they mark the highest and lowest 25% of the distribution.



This document is linked from Normal Random Variables and from Population Means (Part 1).