Normal Probability, psychology homework help

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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). 

See table attached.

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 Empirical Rule (also called the 68-95-99.7 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 Doc Sharing), what percentage of students will likely get a score below this value? What percentage of students are 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

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