Question

The Graduate Record Exam (GRE) has a combined verbal and quantitative mean of 1000 and a standard deviation of 200. Scores range from 200 to 1600 and are approximately normally distributed. For each of the following problems: (a) Indicate the percentage or score called for by the problem.(b) draw a rough sketch, darkening in the portion of the curve that relates to the answer, and1) What percentage of the persons who take the test score above 1300?2) What percentage score above 800?3) What percentage score below 1200?4) Above what score do 20% of the test-takers score?5) Above what score do 30% of the test-takers score?

Answer 1

1.)6.68% ; 2)84.13% ; 3)84.13% ; 4)1168 ; 5)1105

Explanation:

Given a normal distribution with:

Mean (m) = 1000

Standard deviation (sd) = 200

1) What percentage of the persons who take the test score above 1300?

X = 1300

Zscore = (x - m) / sd

Zscore = (1300 - 1000) / 200 = 300/200 = 1.5

P(z > 1.5) = 1 - p(z < 1.5) ;

From the z distribution table:

p(z < 1.5) = 0.9332 ; 1 - 0.9332 = 0.0668 = 6.68%

2) What percentage score above 800?

X = 800

Zscore = (x - m) / sd

Zscore = (800 - 1000) / 200 = - 200/200 = - 1

P(z > - 1) = 1 - p(z < - 1) ;

From the z distribution table:

p(z < - 1) = 0.1587 ; 1 - 0.1587 = 0.8413 = 84.13%

3) What percentage score below 1200?

X = 1200

Zscore = (x - m) / sd

Zscore = (1200 - 1000) / 200 = 200/200 = 1

p(z < 1)

From the z distribution table:

p(z < 1) = 0.8413 = 84.13%

Above what score do 20% of the test takers score?

P(z > Zscore) = 0.2 = P(z > Zscore) = 1 - 0.2 = 0.8

P(z < Zscore) = 0.8

0.8 is closest to a Zscore of 0.84

From the formula:

Zscore = (x - m) / sd

0.84 = (x - 1000) / 200

168 = x - 1000

x = 168 + 1000 = 1168

Above what score do 30% of the test takers score?

P(z > Zscore) = 0.3 = P(z > Zscore) = 1 - 0.3 = 0.7

P(z < Zscore) = 0.7

0.8 is closest to a Zscore of 0.525

From the formula:

Zscore = (x - m) / sd

0.525 = (x - 1000) / 200

105 = x - 1000

x = 105 + 1000 = 1105