Review post and evaluate their solutions for their selected GRE score (number 4). Are the student's calculations correct? If yes, note this and if not correct them with an example. Next, determine what percentage of students will likely get a score above the value the student selected. What happens when you combine your percentage with the percentage they listed for below?

What does "normally distributed" mean in regard to the GMAT, LSAT and GRE admission tests?

A normal distribution is where data maintains some form of symmetry around its mean, creating a bell-shaped visual display that tapers off to the left and right of center.

1a) Why is the data normally distributed?

Because by converting the quantitative data (scores) from the GMAT, LSAT, and GRE into a z-score, you could determine the probabilities of various values and their distance away from the mean.

2) Additional Example of stock market performance and Modern Portfolio Theory (MPT) and why I believe the data is normally distributed.

In short, MPT is a quantitative approach to investing that attempts to mitigate risk and enhance returns by measuring how certain holdings within a portfolio will perform compared to other assets held in that portfolio. By the measurements used, a portfolio's risk can be calculated as the standard deviation from the mean of the total portfolio.

3) Suppose that the mean GRE score for the United States 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 below 275?

The answer is 0.0013.

3a) Is a score below 275 significantly different from the mean?Whyor why not?

Yes, a score of 275 significantly differs from the mean. This isbecausethe likelihood of a student scoring below 275 is only 0.0013 or 13%.

4) Choose any GRE score between 200 and 800. Using your chosen score, how many standard deviations from the mean is your score?

Choosing the value 450. Using a mean of 500 and a standard deviation of 75, I come up with a Z-score of -0.6667, indicating 450 is a -0.6667 standard deviation below the mean of 500.

4a) Using the z-table, what percentage of students will likely get a score below this value?

Using a score of 450 the probability of a student scoring below this number is 0.2525 or 25.25%