Answer:
A) 21%
B) 66%
C) 50%
D) 50%
Step-by-step explanation:
A) We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 5%.
Now, it means we are looking for the value of z on the 5th percentile.
Now from the Z-score percentile normal distribution table i have attached, the value of z on the 5th percentile is; Zx = -1.645
Now, using the regression method, we know that;
Zy = r(Zx)
Where Zy is the score at which the final percentile occurs.
And r = 0.5 from the question
Thus; Zy = 0.5 x -1.645
Zy = - 0.8225
Now looking at the table attached, there is no direct value of -0.8225,and so we pick the closest to it which is -0.8 and it falls on the 21st percentile.
Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 5% would be 21%.
B) We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 80%.
Following same pattern in A above;
From table, Zx = 0.842
And Zy = 0.5 x 0.842 = 0.421
The percentile for this value is approximately 66th percentile.
Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 80% would be 66%.
C)We want to find the percentile rank on the final for a student whose percentile rank on the midterm is 50%.
Following same pattern in A above;
From table, Zx = 0
And Zy = 0.5 x 0 = 0
The percentile for this value is 50th percentile.
Thus, the percentile rank on the final for a student whose percentile rank on the midterm is 50% would be 50%.
D) If the score is unknown, the best bet will be to use a middle percentile of 50%.
It thus follows the same procedure from c above and same answer of 50%.
