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

U.S. graduate schools. Students scores on the quantitative portion of the GRE

follow a normal distribution with mean 150 and standard deviation 8.8. (Source:

http://www.ets.org/.) A graduate school requires that students score above 160 to

be admitted.

a. What proportion of combined GRE scores can be expected to be over 160?

b. What proportion of combined GRE scores can be expected to be under

160?

c. What proportion of combined GRE scores can be expected to be between

155 and 160?

d. What is the probability that a randomly selected student will score over

145 points?

e. What is the probability that a randomly selected student will score less

than 150 points?

f. What is the percentile rank of a student who earns a quantitative GRE

score of 142?