Probability

Advice

• Teach as little as possible.  I only try to get the students to understand independent events versus conditional probability.  Conditional probability is needed for p-values.
• I'd go even farther. Students don't really need to know probability beyond some development of their common understanding. I discuss the idea that it's a measure of how certain we are, work a bit with relative and subjective probabilities and jump to random variables.
• I also try to minimize the probability content. I teach the basic rules using contingency tables. This is more visual and also gives them practice in how to interpret tables of information.
  
• I have been using a book(Devore and Farnum Applied Stats for Engineers and Scientists) that avoids formal probability for awhile and talks about proportions instead.  It works pretty well.  I agree with the minimizing probability.
• Check out this website from an AP-Stat discussion forum that contains very good advice about teaching probability in a statistics class. This applies to college statistics classes too.
• Mutually exclusive vs. Independent
• If you do cover these topics, students will generally have difficulty understanding the difference between the two. Giving examples will help; see this website from an AP-Stat discussion forum for one.
  

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Normal Distribution

Applets

• This applet has a slider so that you can change the mean and standard deviaiton of the normal distribution and see in real time how these changes affect the graph of the normal curve.
• Comparing a general normal distribution to the standard normal distribution. This Wolfram demonstration allows you to continuously change the values of mu, sigma, and z and displays the standard normal curve alongside the general distribution for comparison.
  
• Normal approximation to the binomial distribution. This Wolfram demonstration allows you to continuously change the values of n and p using sliders and it displays the corresponding binomial distribution and its normal approximation. This is especially useful to show why the assumptions of np>5 and nq>5 are needed.