Question

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?

Answer 1

32 and 47.5%

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%

=