Almost all medical schools in the United States require students to take the Med

Question

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). The exam is composed of three multiple-choice sections (Physical Sciences, Verbal Reasoning, and Biological Sciences). The score on each section is converted to a 15-point scale so that your total score has a maximum value of 45. The total scores follow a Normal distribution, and suppose that in a certain year the mean was 25.3 with a standard deviation of 6.6 . There is little change in the distribution of scores from year to year. (a) What percent (± ± 0.01) of students taking the MCAT had a score over 30 ? %. (b) What percent (± ± 0.01) of students had scores between 19 and 25 ?

Explanation / Answer

Let X be the score of Medical College Admission Test (MCAT) and it follows Normal distribution with mean 25.3 and standard deviation of 6.6.

a)   Pr( X > 30) = 1 - Pr( X < 30) = 1 - 0.761805 = 0.238195

by using MS Excel command '=NORMDIST(30,25.3,6.6,1)'

b) Pr( 19 < X < 25) = 0.311969

by using MS Excel command '=NORMDIST(25,25.3,6.6,1)-NORMDIST(19,25.3,6.6,1)'

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