The verbal part of the Graduate Record Exam (GRE) has a mean (m) of 500 and a standard deviation (s) of 100. Use the normal distribution to answer the following questions and show your work?

a. If we wanted to select only students at or above the 90^th percentile, what verbal GRE score would we use as a cutoff?

b. What verbal GRE score corresponds to a percentile rank of 15%?

c. What verbal GRE score corresponds to a percentile rank of 55%?

d. What is the percentile rank of a verbal GRE score of 628?

e. What is the percentile rank of a verbal GRE score of 350?

f. If we randomly selected 1,500 students who had taken the verbal GRE, how many would we expect to score lower than 250?

g. If we randomly selected 1,500 students who had taken the verbal GRE, how many would we expect to score higher than 750?