For students who graduated from high school in 2013, their SAT math scores were approximately normally distributed

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For students who graduated from high school in 2013, their SAT math scores were approximately normally distributed with a mean of 514 points and a standard deviation of 118 points (Source: College Board).
a. If a student is randomly selected from those who graduated from high school in 2013 and took the SAT, what is the probability that the student scored between 600 and 700 points on the math sections?
b. The mean SAT math score for psychology majors was 490 points. Find the percentile for 490 points. A student says that all psychology majors’s SAT math scores are at the percentile you found. What would you tell the student?
c. The mean SAT math scores for social-science majors and engineering majors were 553 points and 580 points, respectively. Find the percentiles for 553 points and 580 points. What is surprising about your results?
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