There are two college entrance exams that are often taken by students, Exam A an
ID: 3201827 • Letter: T
Question
There are two college entrance exams that are often taken by students, Exam A and Exam B. The composite score on Exam A is approximately normally distributed with mean 21.3 and standard deviation 5.3. The composite score on Exam B is approximately normally distributed with mean 1021 and standard deviation 205. Suppose you scored 24 on Exam A and 1220 on Exam B. Which exam did you score better on? Justify your reasoning using the normal model.
Choose the correct answer below.
A. The score on Exam B is better, because the percentile for the Exam B score is higher.
B. The score on Exam A is better, because the difference between the score and the mean is lower than it is for Exam B.
C. The score on Exam B is better, because the score is higher than the score for Exam A.
D. The score on Exam A is better, because the percentile for theExam A score is higher.
Explanation / Answer
in comparing the results which ever score has better z score or percentile, that score would be relatively better.
hence z score of exam A =(X-mean)/std deviation =(24-21.3)/5.3 =0.5094
and z score of exam B =(X-mean)/std deviation =(1220-1021)/205 =0.9707
therefore option A is correct.