Answer:
Student who took ACT appears to be more qualified.
Step-by-step explanation:
We are given that Student A took the ACT and got a score of 24, while student B got an SAT score of 1100.
The year they took their tests, the ACT had an average score of 20.8 and a standard deviation of 5.6, while the SAT had an average score of 1060 and standard deviation of 195.
We have to check which student appears more qualified.
<u><em>We will do this by finding the z scores for both the students and the student with higher z score is considered to be more qualified.</em></u>
<u><em /></u>
The z score probability distribution for a normal distribution is given by;
Z = 
~ N(0,1)
where, 
= average score
= standard deviation
Let X = score of the student
- <u>Student z score who took the ACT is given by;</u>
For this student : X = score of ACT = 24
= average score for ACT = 20.8
= standard deviation for ACT = 5.6
So, z score =
= 
= 0.571
Hence, the student who took ACT has a z score of 0.571.
- <u>Student z score who took the SAT is given by;</u>
For this student : X = score of SAT = 1100
= average score for SAT = 1060
= standard deviation for SAT = 195
So, z score =
= 
= 0.205
Hence, the student who took SAT has a z score of 0.205.
<u><em>Therefore, it is clear that the z score for ACT is higher than that of SAT which means that student who took ACT appears to be more qualified.</em></u>
