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2. The MCAT, Medical College Admissions Test, must betaken by students wishing to gain entrance to most Medical Programsin Canada and the United States. There are four sections: PhysicalSciences (PS), Verbal Reasoning (VR), Biological Sciences (BS), andWriting Sample (WS). The first three are each scored on a scalefrom 1 to 15, with a mean of 8 and a standard deviation of2.

(a) Determine the percentile ranks for the followingstudents:

Name	Physical Science	Verbal reasoning	Biological Science
Jeanine	5	13	11
Louise	6	12	9
Jim	14	10	4

(b) If a Medical School sets a requirement that studentswho will be considered must have a score of 10 on the PhysicalScience, 12 on the Verbal Reasoning and 11 on the BiologicalSciences sections, what proportion of the population will qualifyfor each portion of the test?

c) The ACT, American Colleges Test, is comparable to theSAT Reasoning Test. The ACT is well modeled by a normaldistribution, X~ N(21, 52 ), whereas the SAT Reasoning Test ismodeled by S~N(1500, 3002 ). A college will accept either the SATor the ACT for admissions. A college admissions assistant needs tocompare the following two students to each other though they wrotedifferent tests. How would the admissions assistant do this? Whichstudent seemed to score better? Matthew Chant ACT Score = 27 JosephBell SAT Score = 2050