Each
-score is calculated using the formula
where
is the student's score,
is the class average, and
is the class standard deviation.
So, if you substitute Carol's results, you get that
.
Doing the same for Zachary and Matilda, you will have three equations with only two unknowns. So, you can find what value of
and
work for two of them, and then figure out for the third whether the problem is an incorrect
or
and then find the correction that is needed.