Question

The ACT college readiness assessment is a curriculum- and standards-based educational and career planning tool that assesses students academic readiness for college. Scores are based on a normal distribution with a mean of 23 and a standard deviation of 4. Little Flower University would like to offer an honors scholarship to students who score in the top 10% of this test. What is the minimum score that qualifies for this scholarship? James, Luke and Alexia score 24, 26 and 30 respectively who will get a scholarship offer?

Can you show me the full work out so I can understand it please.

Answer 1

Solution:
Scores are based on a normal distribution with
Mean ()= 23
Standard deviation ()= 4
Also given that Little Flower University would like to offer an honors scholarship to students who score in the top 10% of this test, so p-value = 0.90
From Z table we found Z-score = 1.2816
So Score for an honors scholarship to students can be calculated as
X = + Z-score * = 23 + 1.2816 * 4 = 23 + 5.13 = 28.13
So Scores requried for an honors scholashipe to student should be more than 28.13
Here we can see that James score = 24
Luke Score = 26
Alexia Score = 30
So Alexia will get a scholarship offer because score is more than 28.13.