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Answer :
Final answer:
To find the actual SAT score corresponding to the 72nd percentile, we can convert the percentile to a z-score and use that to calculate the SAT score.
Explanation:
To find the actual SAT score corresponding to the 72nd percentile, we need to convert the percentile into a z-score and then use that z-score to find the corresponding SAT score. The formula to convert a percentile to a z-score is:
z = (X - mean) / standard deviation
Plugging in the values for the SAT test, the z-score corresponding to the 72nd percentile is approximately 0.655. So we can calculate the actual SAT score as follows:
SAT score = (z * standard deviation) + mean = (0.655 * 203) + 1085 = 1338.765
Therefore, the actual SAT score corresponding to the 72nd percentile is approximately 1339.
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