For students who graduated from high school in 2013, their ACT English scores had a mean of 20.2 points and a standard deviation of 6.5 points.
a. Assuming the ACT English scores are normally distributed, find the percentiles for the following scores (in points): 15, 25, and 35.
b. Table 31 displays some of the percentiles by assuming normality and all of the actual percentiles for various ACT English scores. Use your results of part (a) to fill in the blanks.

c. Compare the percentiles assuming normality and the actual percentiles in your completed Table 31. Does your comparison suggest that the ACT English scores are normally distributed, approximately normally distributed, or not at all normally distributed? Explain.

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Table 31 Percentiles by Assuming Normality and Actual Percentiles for Various ACT English Scores Percentile (Assuming Normality) English Score 10 15 20 25 30 35 Actual Percentile 26 52 79 92 100 49 93