Question

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?

Answer 1

The Empirical Rule is saying that 68% of students are only 1 std deviation from the mean, 95% are 2 std deviations from the mean.

Find how many std deviations 350 and 650 are from the mean of 500.
350 - 500 = -150    ----> -150/75 = -2
650 - 500 = 150    ----> 150/75 = 2

Each are 2 std deviations from the mean. This means that about 95% of students are between 350 and 650.

By definition, 50% will be above the mean and below the mean.
Therefore 50% of the students will get a score above 500.