You're looking for 
such that
Transforming the standard normal distribution, you have
where
is the cutoff score in terms of this new distribution. The z-score corresponding to a probability of 0.20 is approximately 
, which means the cutoff test score is
Rounding to the nearest whole point, a score of about 114 is the bare minimum requirement to not have to take the remedial course.
Transforming the standard normal distribution, you have
where
Rounding to the nearest whole point, a score of about 114 is the bare minimum requirement to not have to take the remedial course.