The scores on a psychology exam were normally distributed with a mean of 56 and a standard deviation of 6. 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?

32 and 47.5%

Step-by-step explanation:

Given that X-scores on a psychology exam were normal

X:N (56,6)

Failing grade is 2 or more std deviations below the mean

Mean = 56

2 std deviations = 12

Mean-2 std dev = 56-2 (12)

=56-24

=32

Hence failing score cutoff is 32

I. e. if a student scores less than 32, he is deemed to have failed in the exam

Percentage of students failed = 100*P (X<32)

= P (Z<-2)

=100 (0.475)

=47.5%

=