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 and standard deviation 2.5. For applicants who actually entered medical school, the mean score was 10.4 and the standard deviation was 1.4.
(a) What percent of all applicants had scores higher than
12?
(b) What percent of those who entered medical school had scores
between 10 and 11?
(a)
Given that ,
mean = = 9
standard deviation = = 2.5
P(x > 12) = 1 - P(x < 12)
= 1 - P[(x - ) / < (12 - 9) / 2.5]
= 1 - P(z < 1.2)
=1 - 0.8849
= 0.1151
Answer = 11.51%
(b)
mean = = 10.4
standard deviation = = 1.4
P(10 < x < 11) = P[(10 - 10.4)/ 1.4) < (x - ) / < (11 - 10.4) / 1.4) ]
= P(-0.29 < z < 0.43)
= P(z < 0.43) - P(z < -0.29)
= 0.6664 - 0.3859
= 0.2805
Answer = 28.05%
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