HW Specic Instructions 1. For the probability problems include the appropriate p
ID: 3179981 • Letter: H
Question
HW Specic Instructions
1. For the probability problems include the appropriate probability statements [Ex. P(A|B), P(X = 15), P(3 X < 5), etc.]
2. Use appropriate notation.
3. ALL probabilities MUST be reported in 4 decimal digits.
4. You must use the Z-table to compute the probabilities.
As a part of the application process, most graduate programs require applicants to submit their Graduate Record Examinations (GRE) score (S). The GRE test is a standardized multiple choice test designed to measure the intellectual aptitude of a person. The Educational Testing Service (ETS) who administers the test reported that the average (scaled) score on the quantitative section of the test is 150 with a standard deviation of 6 points. They also claim that S follows closely a normal distribution.
(a) What percentage of those who take the GRE test score at least 159 on the quantitative section?
(b) What is the probability that a randomly selected student will have a (scaled) GRE score on the quantitative section that exceeds 145 but is less than 163?
(c) Suppose that a program considers for admission only students whose score on the quantitative section places them among the top 4%. What is the minimum score one has to score in order to be considered for admission by the particular program
Explanation / Answer
Answer:
As a part of the application process, most graduate programs require applicants to submit their Graduate Record Examinations (GRE) score (S). The GRE test is a standardized multiple choice test designed to measure the intellectual aptitude of a person. The Educational Testing Service (ETS) who administers the test reported that the average (scaled) score on the quantitative section of the test is 150 with a standard deviation of 6 points. They also claim that S follows closely a normal distribution.
(a) What percentage of those who take the GRE test score at least 159 on the quantitative section?
Z value for 159, z =(159-150)/6 =1.5
P( x 159) = P( z >1.5)
=0.0668
(b) What is the probability that a randomly selected student will have a (scaled) GRE score on the quantitative section that exceeds 145 but is less than 163?
Z value for 145, z =(145-150)/6 =-0.83
Z value for 163, z =(163-150)/6 =2.17
P(145< X < 163) = P( -0.83<z<2.17)
=P( z <2.17) –p( z <-0.83)
=0.985-0.2033
=0.7817
(c) Suppose that a program considers for admission only students whose score on the quantitative section places them among the top 4%. What is the minimum score one has to score in order to be considered for admission by the particular program
Z value for top 4% = 1.751
X =150+1.751*6
=160.506
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