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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

No Standard Deviation? How do I get the standardized test statistic?

I get this question a lot in my BUS 233 Business Statistics course. It comes when students see a problem similar to the following in their homework or on a quiz:

In a sample of 1000 home buyers, you find that 457 home buyers found their real estate agent through a friend. At α=0.08, can you reject the claim that 50% of home buyers find their real estate agent through a friend?
a) Write the claim mathematically and identify H0 and Ha. (b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis.

If you run into a problem which asks you to find the standardized test statistic but does not give you the standard deviation, it is probably a proportion problem and this one is just that.

Solution:

Ho: p = 0.50; Ha: p ≠ 0.50.

No Standard Deviation? How do I get the standardized test statistic?