(Solved): 18. Suppose that the distribution of scores on the Graduate Record Exam (GRE) is approximately norm ...

18. Suppose that the distribution of scores on the Graduate Record Exam (GRE) is approximately normal, with a mean of \( \mu=150 \) and a standard deviation of \( \sigma=5 \). For the population of students who have taken the GRE: a. What proportion have GRE scores less than 145 ? b. What proportion have GRE scores greater than 157 ? c. What is the minimum GRE score needed to be in the highest \( 20 \% \) of the population? d. If a graduate school accepts only students from the top \( 10 \% \) of the GRE distribution, what is the minimum GRE score needed to be accepted?