Question

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). A new version of the exam was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded has been modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015 the mean score was 500.0 with a standard deviation of 10.6 Use Table A to find the answers to the two questions. (a) What proportion of students taking the MCAT had a score over 520? Compute the proportion and then enter the answer as a percentage rounded to two decimal places percentage over 520- b) What proportion of students taking the MCAT had scores between 515 and 525? Compute the proportion and then enter the answer as a percentage rounded to two decimal places percentage between 515 and 525-

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

mean = 500

standard deviation = 10.6

(a) P(X > 520) = 1 - P(X < 520)

= 1 - P(Z < (520 - 500)/10.6)

= 1 - P(Z < 1.89)

= 1 - 0.9706 (from standard normal distribution table)

= 0.0296

Percentage over 520 = 2.96 %

(B) P(515 < X < 525) = P(X < 525) - P(X < 515)

= P(Z < (525 - 500)/10.6) - P(Z < (515 - 500)/10.6)

= P(Z < 2.36) - P(Z < 1.42)

= 0.9909 - 0.9222

= 0.0687

Percentage between 515 and 525 = 6.87 %