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In the year 2016, the average SAT in NYS score was 1125 with a standard deviation...

In the year 2016, the average SAT in NYS score was 1125 with a standard deviation of 100. A student from a NYS high school received a 1215 during that year. In the year 2017, the average SAT score in NYS was 1150 with a standard deviation of 35. A student in NYS during the 2017 year received an 1195. Which student will have a higher percentile rank? Explain what caused this to happen

Math   Statistics-And-Probability   
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Answer #1

The z-score of the student in the year 2016 = (X - )/

                                                                        = (1215 - 1125)/100 = 0.9

The z-score of the student in the year 2017 = (X - )/

                                                                        = (1195 - 1150)/35

                                                                        = 1.29

So the student in the year 2017 will have a higher percentile rank, because the z-score of the student in the year 2017 is higher than the z-score of the student in the year 2016.

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