1.Students wishing to gain entrance to universities and colleges in the United States must complete the SAT Reasoning Test(1) There are three parts to the test: Writing, Mathematics and Critical Reading. Each part of the test has a mean of approximately 500, a standard deviation of 100 and is well modeled by the normal distribution. Answer the following questions based on these results.

(a)Three students wrote their SATs and obtained the following scores. Determine their percentile for each part of the test.

Name

Writing

Mathematics

Critical Reading

Joseph

450

642

579

Kaylyn

745

562

629

Larissa

327

437

575

(b)Sometimes the total score is used. In 2006, the mean total score was 1518 and the standard deviation was 308. Determine the percentile rank for each of these students.

(c)Based on the total score, X ~ N(1518, 308²), a University has required that students who would be considered for acceptance must score at least 2000 on the SAT Reasoning Test. What proportion of students would score 2000 or higher?

(d)In order to gain acceptance to a particular College program, prospective students must be at the 87^th percentile in Writing, the 90^th percentile in Critical Reading and the 75^th percentile in Mathematics. Determine the minimum scores that students need to meet these requirements.

(1) Triviathe SAT was originally the Scholastic Aptitude Test, was renamed to the Scholastic Assessment Test, and finally to the SAT Reasoning Test, to avoid the association between the test score and innate intellectual ability.

2.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, 12 on 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 Reasoning Test. 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 ChantACT Score = 27 Joseph BellSAT Score = 2050