Question

1. The NCAA considers a student a “partial qualifier” – eligible to practice and receive scholarship money but not compete – if his/her combined SAT score is at least 720. What percentage of students would be partial qualifiers only?
2. The NCAA requires Division 1 athletes to get a combined score of 820 on their Math and Verbal skills tests in order to compete their first year in college. The scores for the 1.4 million students who took the test last year were normally distributed with an average of 1026 and a standard deviation of 209. What percentage of the students would have qualified as Div 1 athletes?

Answer 1

General Approach to solve these types of questions.

1) find the mean and std. deviation of normal distribution

2) find z value for all the data needed.

3) from normal distribution table calculate probability

4) convert probability into percentage by multiplying it by 100.

Note. Assumption

A) partial qualifier only includes those having score between 720 and 820

2) Div 1 atheletes are those having score above 820.

3) SAT score includes only math and verbal skills.

Solution: