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.
- 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 Problems- Two Common Mistakes