Question

The scores for all high school seniors taking the verbal section of the Scholastic Aptitude Test (SAT) in a particular year had a mean score of 490 and a standard deviation of 100. The distribution of SAT scores is bell-shaped.

What does the Empirical Rule suggest?
About 68% of students scored between what 2 values?
About 95% of the students scored between what 2 values?
What percentage of seniors scored between 390 and 590 on this SAT test?
One student scored 795 on this test. How did this student do compared to the rest of the scores

Answer 1

The Empirical Rule indicates that about 68% of students scored between 390 and 590, about 95% scored between 290 and 690 on the SAT verbal section, and a student scoring 795 performed exceptionally well being over 3 standard deviations above the mean.

Step-by-step explanation:

The Empirical Rule, also known as the 68-95-99.7 rule, applies to bell-shaped distributions. It states that about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

About 68% of students scored between 390 and 590 on the SAT test (490 ± 1×100). About 95% of the students scored between 290 and 690 (490 ± 2×100).

For the SAT scores between 390 and 590, this range encompasses one standard deviation from the mean, so approximately 68% of seniors scored within this range.

A student scoring 795 is 3.05 standard deviations above the mean (795-490)/100, which is highly exceptional, as it's beyond the range where 99.7% of scores lie according to the Empirical Rule.