Need help with my Statistics Homework about a normal probability curve

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 portion to assist you with
answering the Discussion topics. There is a full z table in Doc Sharing.

Standard Scores and Percentiles.jpg

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 in Doc Sharing. There is a tutorial that can assist located in Doc
Sharing.