Question

The GRE scores for Writing section in Illinois are known to be normally distributed with a mean score of 525 and a standard deviation of 57.2.

Student A’s score was 439; calculated z-score is ______ and its corresponding percentile rank is ______ (in the scale of percentage, e.g. XX.XX).

Student B’s score was 580; its z-score is ______ and its corresponding percentile rank is ______.

And, student C’s score was 635; its z-score is ______ and its corresponding percentile rank is ______. (Calculate to the nearest two decimals)

Answer 1

Given that, mean (μ) = 525 and standard deviation = 57.2

For student A's score = 439

z = (439 - 525) / 57.2 = -1.50

P(Z < -1.50) = 0.0668 (OR 6.68%)

For student B's score = 580

z = (580 - 525) / 57.2 = 0.96

P(Z < 0.96) = 0.8315 (OR 83.15%)

For student C's score = 635

z = (635 - 525) / 57.2 = 1.92

P(Z < 1.92) = 0.9726 (OR 97.26%).

Therefore,

Student A’s score was 439; calculated z-score is -1.50 and its corresponding percentile rank is 6.68%.

Student B’s score was 580; its z-score is 0.96 and its corresponding percentile rank is 83.15%.

And, student C’s score was 635; its z-score is 1.92 and its corresponding percentile rank is 97.26%.