if the mean of sat scores is 1900 and the std dev is 100 what do you have to make to be in the upper 16%

Question

if the mean of sat scores is 1900 and the std dev is 100 what do you have to make to be in the upper 16%

Answer 1

This is based on the normal curve, which has a specific percentage of test scores within each range of standard deviation. The mean is the exact middle or high point of the curve, so that 50% of scores are higher & 50% are lower than 1900. The normal curve is always arranged so that +1 standard deviation is about 34.1%, +2 st. dev. is about 13.6%, and +3 SD is about 2.15% of all data. Negative 1, 2, and 3 SD are, therefore, the same percentages on the lower half of the curve. +/-4 SD are a small percentage of outliers on each end of the curve.

34.1% (1 SD) should be a big clue to this solution - 15.9% of scores are more than 1 SD from the mean. Since +1 SD represents up to 100 points above the mean, we add 100 to 1900 to yield a score of 2000. Therefore, 15.9% of scores are above 2000. You could say that scores of 2000 & above are in the upper 16%.