Suppose during the ironic retake of MCAT (Medical College Admission Test) this y
ID: 3364626 • Letter: S
Question
Suppose during the ironic retake of MCAT (Medical College Admission Test) this year, the students can either submit only their second attempt (att-2) score or their first attempt score (att-1), provided if the marks are higher, to a particular college. The second way a student can apply is through the test conducted by NTS (National Testing Service), an exemption made due to the non-clarity and confusion surrounding the MCAT test. Suppose a student’s att-1 score was 720 and that the att-1 has a mean of 600 and a standard deviation of 100. Suppose also that the same student scored an 800 on their second attempt of the same exam and that the att-2 has a mean of 770 and a standard deviation of 150. And the same student scores 67 marks in NTS, with a percentile of 73%, it has a mean of 58 with a standard deviation of 5. Which score should the student submit?
Explanation / Answer
Z score = (X - u)/s where X is attained score
u is the mean and s is standard deviation
Z score for attempt 1= (720 - 600)/100 = 1.2
Z score for attempt 2 = (800 - 770)/150 = 0.2
Z score for NTS = (67 - 58)/5 = 1.8
This shows that the probability of score higher than other aspirants taking the same test is highest in case of NTS
which can be clearly seen from Z table.
But here the percentile of 73% is given in case of NTS whereas Z table gives probability of 96.41% that the score is higher than other aspirants. This is because percentile is calculated taking median as average which means that the median is higher than mean.
This means the distribution of NTS scores are negativelt skewed.
But as no percentile is given for MCAT test, we assume the distribution to be normal, Thus attemp 1 fetches highest probability of 88.49%.
Thus MCAT attempt 1 score should be submitted by the student