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

- What is the probability a randomly selected credit card holder has a card balance less than $2500?
- You randomly select 25 credit card holders. What is the probability that their mean card balance is less than $2500?
- 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: [Read more…] about Normal Distribution Problem- Two Common Mistakes