Almost all medical schools in the United States require applicants to take the M

Question

Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately normal with mean 9.1 and standard deviation 2.2. For applicants who actually entered medical school, the mean score was 10.8 and the standard deviation was 1.5. Note: Enter your answers in the form 74.22%, not 0.7422.

(a) What percent of all applicants had scores higher than 12?
ANSWER:    %

(b) What percent of those who entered medical school had scores between 10 and 11?
ANSWER:    %

Explanation / Answer

a) MCAT -

mean = 9.1 , sd = 2.2

Z = (X -mean)/sd =(X - 9.1)/2.2

P(X > 12) = P(Z> (12 -9.1)/2.2) = P(Z> 1.32) = 0.0934

= 9.34%

b) Those who entered medical colleg

mean = 10.8 ,sd = 1.5

P(10<X<11)

= P( -0.53 < Z< 0.13)

= 0.2536

hence 25.36 %

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