Discussion Questions

1. Describe the key features of the normal curve and explain why the normal curve in real-life distributions never matches the model perfectly.

2. Imagine that you recently took a statistics exam and your instructor just returned your graded exam. The instructor announces that 75% of students scored below the mean. How do you reconcile this with the fact that, in a normal distribution, half of the scores should fall below the mean and half of the scores should fall above the mean?

3. Compare and contrast an empirical distribution and a normal distribution. Describe the value of each distribution. Discuss the terminology that is invoked to denote the former and the terminology that is invoked to denote the latter.

4. According to the material presented in chapter 6, why do researchers use Z scores? What are the advantages of using Z scores? Describe some research questions that would require the use of Z scores. Are there any research questions that would not be appropriate for the use of Z scores?

5. Why can we NOT assume that for any scale variable, 50% of cases are above the mean and 50% are below the mean?

6. Why do we use a bell curve to assess the normality of a variable as opposed to a square, triangle, or some other symmetrical shape?