Homework6: Problem 5 Previous Problem List Next (1 point) Almost all medical sch

Question

Homework6: Problem 5 Previous Problem List Next (1 point) 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 9.4 and standard deviation 2.1. For applicants who actually entered medical school, the mean score was 10.5 and the standard deviation was 1.7. 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 9 and 11? ANSWER: Note: You can earn partial credit on this problem.

Explanation / Answer

Solution:-

Given that : all applicants Mean = 9.4 and standard deviation = 2.1
medical school = mean = 10.5 standard deviation = 1.7

a) all applicants had scores higher than 12 is 10.75%
P(X > 12) = P(Z > (X-)/)
= P(Z > (12-9.4)/2.1)
= P(Z > 1.2381)
= 0.1075
= 10.75%

b) The percent of entered medical school had scores between 9 and 11 is 42.47%
P(9 < X < 11) = P((9-10.5)/1.7 < Z < (11-10.5)/1.7)
= P(-0.8824 < Z < 0.2941)
= 0.4247
= 42.47%

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