For students who graduated from high school in 2013, their SAT math scores had a mean of 514 points and a standard deviation of 118 points.
a. Assuming the SAT math scores are normally distributed, find the percentiles for the following scores (in points): 400, 600, and 800.
b. Table 30 displays some of the percentiles by assuming normality and all of the actual percentiles for various SAT math scores. Use the results you found in part (a) to fill in the blanks.

c. Compare the percentiles assuming normality and the actual percentiles in your completed Table 30. Does your comparison suggest that the SAT math scores are normally distributed, approximately normally distributed, or not at all normally distributed? Explain.

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Table 30 Percentiles by Assuming Normality and Actual Percentiles for Various SAT Math Scores Percentile Actual Math Score (Assuming Normality) Percentile 300 400 500 600 700 800 16 45 75 93 45 94