Question

Scores on the verbal portion of the GRE follow a normal distribution with a mean of 500 and standard deviation of 115.

Question: The middle 95% of the scores fall between a low score of and a high score of ______________

Answer 1

Given:

Mean, =500

Standard deviation, =115

For 95% or 0.95 area in the middle, the corresponding low and high Z-scores are -1.96 and +1.96 respectively.

Z =(X - )/X =Z +

Low score =X1 = -1.96(115) + 500 =274.6

High score =X2 = +1.96(115) + 500 =725.4

Answer: The middle 95% of the scores fall between a low score of and a high score of 274.6 and 725.4 respectively.