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Normal Distribution Problems- Two Common Mistakes

I see many students in my intro statistics courses missing problems related to the normal distribution.

Common Mistake #1: One especially common mistake is not using the correct “standard deviation” to find probabilities and percentiles.

Consider the following problem statement:

A bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900.

  1. What is the probability a randomly selected credit card holder has a card balance less than $2500?
  2. You randomly select 25 credit card holders. What is the probability that their mean card balance is less than $2500?
  3. Interpret the two probabilities in terms of the auditor’s claim.

I usually see students get one of the questions correct, but not all. And they either seem to get #1 or #2 correct in about equal proportions. When I inspect their solutions, I find that they get confused over the “standard deviation” to use in the equation for z.

Most students seem to get #1 correct. They use the formula for z:Normal Distribution Problems- Two Common Mistakes

More on Multiple Regression Part 2

In the real world, we most often work with real data. And we build regression models using software such as Excel, StatCrunch, and, more recently, R. The output of those regressions give us a world of information about the regression models, enabling us to quickly determine if the overall model is statistically significant and if the individual regression coefficients are as well. And with most software, getting confidence intervals associated with the regression model is straightforward.

But in the world of academia, my students often are confronted with an inability to work on the actual data and are instead presented with partial regression output. I know the intent is to make sure students understand the nuts and bolts of regression, but my sense that could be done just as well or better with real data.

That said, I want to help my students learn about regression and get through their academic course with a satisfactory grade.

Here is a typical problem probing understanding of regression intermediates:More on Multiple Regression Part 2