The Graduate Record Examination (GRE) is a test required foradmission to many U.S. graduate schools. Students' scores on thequantitative portion of the GRE follow a normal distribution withmean 150 and standard deviation of 8.8. In addition to otherqualifications, a score of at least 160 is required for admissionto a particular graduate school.
a. What proportion of combined scores can be expected to be over160?
b. What proportion of combined GRE scores can be expected to bebetween 155 and 160?
c. What is the probability that a randomly selected student willscore less than 150 points?
d. Historically, Department of History at NYU has admittedstudents whose quantitative GRE score is at least at the 61stpercentile. What is the lowest GRE score of the students theyadmit?
e. Determine the range of scores that make up the middle 95% ofthe scores.
