Question

(3.12) 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 6.5. 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 31?

%.

(b) What percent (±

0.01) of students had scores between 19 and 25?

Answer 1

Answer:

a)

To determine the percent of students taking the MCAT had a score over 31

Given,

Mean = 25.3

Standard deviation = 6.5

P(X > 31) = 1 - P(Z <= 31 - 25.3 / 6.5)

= 1 - P(Z <= 5.7/6.5)

= 1 - P(Z <= 0.88)

= 1 - 0.811

P(X > 31) = 0.189

P(X > 31) = 18.9 %

b)

To determine the percent of students had scores between 19 and 25

P(19 <= X <= 25) = P(X <= 25) - P(X <= 19)

= P(Z < 25-25.3/6.5) - P(Z < 19-25.3/6.5)

= P(Z < -0.05) - PP(Z < -0.97)

= 0.48 - 0.17

= 0.31

P(19 <= X <= 25) = 31%