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: https://www.ets.org/.) A graduate school requires that students score above 160 to be admitted.
a. Find the Z-score corresponding to the 60th percentile. In other words, find the Z-score such that the area under the standard normal curve to the left is 0.60.
b. How many standard deviations above the mean is the 60th percentile?
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?