mean of 78.4 and 77 percent of the scores are above 90 .The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth, if necessary.

Question

Scores on a test have a mean of 78.4 and 77 percent of the scores are above 90. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth, if necessary.

Answer 1

If 77% of the scores are above 90 they are at least 90-78.4=11.6 above the mean. The Z score corresponding to 77% is 0.74 which means 0.74 standard deviations from the mean, and implies that 77% of the scores are below 90. However, 77% of the scores above 90 means 23% of the scores are below 90. That corresponds to a Z score of -0.74, which is to the left of the mean. The magnitude of the standard deviation is given by 11.6/0.74=15.7 (?)