The Normal Curve

Teaching Tips

• The 68-95-99.7 rule of thumb is a very useful tool for understanding distributions. However, beware of students who will try to apply this rule to everything. It is very important that students be comfortable calculating areas under the normal curve, either by using their calculator, a computer, or a table.

• Make sure students connect the population proportions to the area under the normal curve. Encourage them to sketch the curve and shade the appropriate regions to reinforce this concept.

• Two important technical skills are (1) to go from x values to z-scores to areas under the normal curve and (2) in the other direction: from areas back to x values.

• There are a few books out there that have "idiosyncratic" normal tables. If you're using one of them, make sure your students get to work with an "AP standard" table. For example, those made available by the College Board. Visit http://apcentral.collegeboard.com. The tables in POD and YMS are also good to use.

•The normal probability plot or the normal quantile plot (they are slightly different but for our purposes the differences are neglible) is a useful and commonly used tool for assessing whether or not a sample is plausibly from a normally distributed population. However, these plots are rather complex and difficult to understand, and there's no need to get caught up in the "why" at this point. Learning to interpret the plots is enough.

• It helps to do simulations to get a sense of when a normal probability plot is "straight." There's lots of variability in the tails, and so normal probability plots that stray from a straight-line out at the ends --even quite a bit of straying -- might still be from normal distributions, particularly if the sample size is not too big.