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?

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.