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Mathematics & Economics
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English (U.S.)
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Investigating the Bell Curve in Normally Distributed Data

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In this unit, you will investigate the normal probability curve (the bell curve). Many variables, such as height and weight are "normally distributed." This means, for example, that if you were to collect 10,000 female adult human heights, the histogram of that data would be shaped like a "bell" (with "most" of the data near the center or mean).
Use the following z-table (also located in Course Resources) to assist you with answering the discussion topics.
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. Where appropriate on the questions below, show how you calculate your values.
1. Across the United States, results for these exams are normally distributed. What does that mean, and why is this the case?
2. Other than the GMAT, LSAT, and GRE, provide an example of another normally distributed set of data (you are not limited to student performance exams). Explain why you believe the data are normally distributed.
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? Is a score below 275 significantly different from the mean? Why or why not?
4. Choose any GRE score between 200 and 800. Be creative, choosing unusual scores such as 483. This will allow you to likely 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 also located in Course Resources), what percentage of students will likely get a score below 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,

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1. Across the United States, results for these exams are normally distributed. What does that mean, and why is this the case?
A normal distribution in the results for these types of exams means that the scores of the people who took the test are approaching the mean, whether from the left (lower scores) or from the right (higher scores). This is likely because of similar educational styles or level of teaching, when considering a national score base, where the scores within the average range can be common because, for example, the educational standards are the same for the entire country. This means that the data represents how an average American might likely score in the test based on the results of the many, without considering other internal factors.
2. Other than the GMAT, LSAT, and GRE, provide an example of another normally distributed set of data (you are not limited to student performance exams). Explain why you believe the data are normally distributed.
Another example is the height of males in the USA. I believe this is the case because despite there being a diverse population and some exceptional examples for individuals being in the shorter and taller end of the data points, the heights of ...
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