Question

3. Suppose that the mean GRE score for the United States is 500 and thestandard deviation is 75. Use the 68-95-99.7 (empirical) rule to determinethe percentage of students likely to get a score below 275? Is a score below275 significantly different from the mean? Why or why not?

Answer 1

The 68-95-99.7 rule states that

68% of the data will fall within 1 standard deviation of the mean that is

500 + 1*75 = 575, and 500 - 1*75 = 425

95% of the data will fall within 2 standard deviation of the mean that is

500 + 2*75 = 650, and 500 - 2*75 = 350

99.7% of the data will fall within 3 standard deviation of the mean that is

500 +3*75 = 725, and 500 - 3*75 = 275.

The percentage of students likely to get a score below 275 is (100% - 99.7%) = 0.3%

The further the score is to the mean, the less likely it is to happen. The score 275 is within 3 standard deviation away from the mean, which means that a score below 275 IS significantly different because 99.7% of the students are between 275, and 725.