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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

When do I substract from 1?

Always sketch the normal curve situation first. Remember the Standard Normal Distribution tables almost always give the area/probability from left infinity to the z-value in question; check for sketches on the tables you use to… When do I substract from 1?