The Graduate Record Examination (GRE) is a test required for admission to many U

Question

The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with a mean of 150 and a standard deviation of 8.8. In addition to other qualifications, a score of at least 152 is required for admission to a particular graduate school.

GRE scores continued:

Using either by hand calculations or technology, answer the following. There may be some small variation between by hand and technology calculations.

What is the percentile rank of a student who earns a GRE score of 142? (hint: in Excel use NORM.DIST function)

Historically, NYU has admitted students whose mean GRE score is in the 61st percentile. What is the mean GRE score of the students they admit? (hint: in Excel use NORM.INV function)

Determine the 80th percentile of GRE scores. (hint: in Excel use NORM.INV function)

Determine the GRE scores that make up the middle 95% of all scores. (hint: in Excel use NORM.INV function)

Compare the results in part d) to the values given by the Empirical Rule.

Explanation / Answer

mena = 150 , s = 8.8

a)
P(X < 140)

z = ( x -mean) /s
= (142 - 150) / 8.8
= -0.9090

P(X < 142) = P(z <-0.9090) = 0.1817 = 18.17%
By using standard table

b)
z value at 61% = 0.2793

z = ( x - mean) / s
0.2793 = ( x - 150) / 8.8
x = 152.45784

c)

z value at 80% = 0.8416

z = ( x - mean) / s
0.8416 = ( x - 150) / 8.8
x = 157.40608

d)

z value at 95% 1.96

CI = mean +/- z * s
= 150 +/- 1.96 * 8.8
= (132.752 , 167.248)

BY empirical rule 95% of data fall within 2 std.dev of mean

= mean +/- 2* std.dev
= 150 +/- 2 * 8.8
= (132.4 ,167.6)

Both results are approx same in above methods

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