The scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 9. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?
Accepted Solution
A:
Given:Sample mean= 57
Standard Deviation= 9 score of 59
we go to our standard formula:
(score - mean) / sd = z (59 - 57) / 9 = z
2/9 = z
0.2222 = z Failing score cutoff would be equal to Mean - 2SD = 67 - 2(9) = 48 is failing score cutoff.