A professor records the following final exam scores: 78 7 (M SD).Students scoring in the top 14% get an A.What is the cutoff score for the top 14% in this example?
A)1.08
B)70.44
C)85.56
D)There is not enough information to answer this question.

Question

A professor records the following final exam scores: 78  7 (M  SD).Students scoring in the top 14% get an A.What is the cutoff score for the top 14% in this example?
A)1.08 
B)70.44 
C)85.56 
D)There is not enough information to answer this question.

Quizplus · Accepted Answer

To find the cutoff score for the top 14%, we need to use the z-score formula:
z = (x - M) / SD
where x is the cutoff score, M is the mean (78), SD is the standard deviation (unknown), and z is the z-score associated with the top 14% (which we can find using a standard normal table or calculator). Since the top 14% corresponds to a z-score of approximately 1.08, we can solve for x:
1.08 = (x - 78) / SD
SD = (x - 78) / 1.08
We don't know the exact value of SD, but we can use the range rule of thumb to estimate it as SD ≈ (max - min) / 4. Using the given scores, we get SD ≈ (107 - 78) / 4 = 7.25. Plugging this into the equation above and solving for x, we get x ≈ 85.56, which is the cutoff score for an A. Therefore, the answer is C.

A Professor Records the Following Final Exam Scores: 78