High School

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admissions. Scores on the SAT test are normally distributed with a mean of 1085 and a standard deviation of 203. Scores on the ACT test are normally distributed with a mean of 20 and a standard deviation of 4.9. It is assumed that the tests measure the same aptitude but use different scales.

If a student gets an SAT score that is at the 72nd percentile, find the actual SAT score.

SAT score: _______

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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