On a recent English exam,scores averaged 77 points.If 2% of scores fell above 95 points,find an approximate standard deviation (assuming the Normal model is appropriate).
A)1.9
B)83.50
C)8.78
D)-8.78
E)1.54

Question

Quizplus · Accepted Answer

To approximate the standard deviation, we can use the empirical rule which states that approximately 95% of the scores fall within two standard deviations of the mean. Since 2% of scores fell above 95, we can assume that those scores were two or more standard deviations above the mean. From this, we can estimate that two standard deviations is equal to (95-77)*2 = 36. Using this value, we can estimate the standard deviation as 36/4 = 9. Therefore, the best choice is C, which is the closest option to 9.

On a Recent English Exam,scores Averaged 77 Points