Question

The MCAT, Medical College Admissions Test, must be taken by students wishing to gain entrance to most Medical Programs in Canada and the United States. There are four sections: Physical Sciences (PS), Verbal Reasoning (VR), Biological Sciences (BS), and Writing Sample (WS). The First three are each scored on a scale from 1 to 15, with a mean of 8 and a standard deviation of 2.

(a)Determine the percentile ranks for the following students:

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

(b)If a Medical School sets a requirement that students who will be considered must have a score of 10 on the Physical Science, 12on the Verbal Reasoning and 11 on the Biological Sciences Sections, what proportion of the population will qualify for each portion of the test?

3.The ACT, American Colleges Test, is comparable to the SAT ReasoningTest. The ACT is well modeled by a normal distribution, X~ N(21, 52),whereas the SAT Reasoning Test is modeled by S~N(1500, 3002). A college will accept either the SAT or the ACT for admissions. A college admissions assistant needs to compare the following two students to each other though they wrote different tests. How would the admissions assistant do this? Which student seemed to score better?

Matthew Chant ACT Score = 27

Joseph BellSAT Score = 2050

Answer 1

Suppose,

• denotes marks in physical sciences.
• denotes marks in verbal reasoning.
• denotes marks in biological sciences.

(a)

Obtained marks are as follows.

Z-scores corresponding to each mark is given by

Thus Z-scores (z) are as follows.

Percentile ranks are given by .

Thus percentile ranks are as follows.

(b)

Students who will be considered must have a score of 10 on the Physical Science, 12 on the Verbal Reasoning and 11 on the Biological Sciences Sections.

Probabilities that students qualify in each portions of Physical Science, Verbal Reasoning and Biological Sciences are as follows.

3.

The admissions assistant may compare using Z-scores as it is standardized value.

Z-score of Matthew Chant ACT Score is given by

Z-score of Joseph Bell SAT Score is given by

Hence, Joseph Bell seems to score better.