Every year, hundreds of thousands of graduating college seniors ponder over one of the most intriguing

questions - what is a good GRE score? The Educational Testing Service gives a general GRE test

percentage distribution of scores by intended graduate field. For the Social and Behavioral Sciences

the mean score for Verbal Reasoning section (Xv ) was 153 with a standard deviation of 8 and the mean

score for the Quantitative Reasoning section (Xq ) was 152 with a standard deviation of 9 . Suppose

that both distributions are nearly normal and the performance on these two sections is independent.

The questions below are for students who intend to study the Social and Behavioral Sciences.

a) [2 points] Assuming you choose to model these scores with normal distributions, write down the distributions

of Xv and Xq , specifying all the parameters.

b) [3 points] What percent of of individuals have a Quantitative Reasoning score greater than 162 ?

c) [3 points] What Verbal Reasoning score should one have to be in the top 10% ?

d) [2 points] The Combined score is the sum of the Verbal Reasoning and Quantitative Reasoning score

(that is, C = Xv + Xq ). What is the mean of the Combined score (that is, E(C) )?

e) [2 points] Using the assumption that performance on these two sections is independent, explain why

the variance of the Combined score is 145 .