Question

PLEASE HELP ASAP!!!!!

Carl, Brian, Dave, and Ashley want to attend the same university. Unfortunately only two spots remain and these four friends have the same GPA, as well as virtually identical community service and leadership experiences. Therefore, the two spots will be determined by their SAT and ACT scores. Carl scored 1,280 on the SAT, while Brian scored 1,325. Dave scored 28 on the ACT, while Ashley scored 30. Use z-scores to determine which two students should be admitted. The mean SAT score was 1,000 with a standard deviation of 175 and the mean ACT score was 20.6 with a standard deviation of 5.2 Both tests are normally distributed.

Answer 1

Use z = (x - μ)/σ for all 4 people.

Carl:

z = (x - μ)/σ

z = (1280 - 1000)/175

z = 1.6

Brian:

z = (x - μ)/σ

z = (1325 - 1000)/175

z = 1.9

Dave:

z = (28 - 20.6)/5.2

z = 1.42

Ashley:

z = (x - μ)/σ

z = (30 - 20.6)/5.2

z = 1.81

Using the z-scores for each student above, the following two students should be admitted into the university:

Brian based on his SAT score and Ashley based on her ACT score.

Answer 2

Calculate the four z-scores pertaining to this data, and then compare them. The two students with the highest z-scores are offered admission.
28-20.6
For Dave: z = ---------------- = 1.42
5.2

Find the z scores for the other 3 students. Rank your results in ascending order. Take the 2 students whose z scores are greater than the remaining z scores.