Question

the mean score of a mathematics placement exam is 125 with a standard deviation of 12.51. those who score i the bottom 20% are required to take a remedial course. assuming the data are not normally distributed, what is the lowest score you can get and not have to take the remedial math class?

Answer 1

You're looking for $k$ such that

$\mathbb P(X$

Transforming the standard normal distribution, you have

$\mathbb P(X$

where $k^*$ is the cutoff score in terms of this new distribution. The z-score corresponding to a probability of 0.20 is approximately $z=k^*=-0.8416$, which means the cutoff test score is

$k^*=\dfrac{k-125}{12.51}\implies k=125+12.51k^*\approx114.47$

Rounding to the nearest whole point, a score of about 114 is the bare minimum requirement to not have to take the remedial course.