Use the following z table portion to assist you with answering the Discussion topics. There is a full z table in Course Resources.

Different university departments use different tests to compare student performance and to determine graduate admission status. Three such tests are the GMAT, the LSAT, and the GRE.

1. Across the USA, results for these exams are normally distributed. What does that mean and why is this the case?
2. If you were to create a histogram of all GRE scores, what would you expect the histogram to look like? Would it be symmetrical? Would it be bell shaped? How many modes would it likely have? Would it be skewed?
3. Suppose that the mean GRE score for the USA is 500 and the standard deviation is 75. Use the 68-95-99.7 (Empirical) Rule to determine the percentage of students likely to get a score between 350 and 650? What percentage of students will get a score above 500? What percentage of students will get a score below 275? Is a score below 275 significantly different from the mean? Why or why not?
4. Choose any GRE score between 200 and 800. Be sure that you do not choose a score that a fellow student has already selected. Using your chosen score, how many standard deviations from the mean is your score? (This value is called the z-value). Using the table above (or the z table in Course Resources), what percentage of students will likely get a score below this value? What percentage of students is likely to get a score above this value?

Hints: The “standard score,” the “z score,” the “z value,” and the “number of standard deviations from the mean” are all saying the same thing. If you cannot find your exact score on the table, use the closest value or use the z table in Course Resources. There is a tutorial that can assist located in Course Resources.

Please create personalized and substantive responses to at least two other student main posts. In your response, include the following:

Choose any two classmates and review their main posts.

1. Review the student post and evaluate their solutions for using the 68-95-99.7 (Empirical) Rule to determine the percentage of GRE scores between 350 and 650. Are the student’s calculations correct? If yes, note this and if not correct them with an example. Next, explain to the student why 50% of the scores are above 500 and why 50% are below (approximately).
2. Review the student’s GRE score choice from number 4 above. Are the student calculations correct? Include the student’s calculations in your response and note any issues if discovered. Then, offer the student a second example using any other value between 300 and 500. Be sure to explain all the steps in your example to the student and to show all work.

Discussion Requirements

Rubrics

Reading and Resources

• Read the assigned chapters from the following textbooks:

Bennett, J., Briggs, W.L. & Triola, M.F. (2013) Statistical Reasoning for Everyday Life (4th ed.). Upper Saddle, NJ: Pearson.

• Chapter 5: “A Normal World”