Let X be the random variable that describes the score of a randomly chosen student. We are told that X is distributed normally distributed with a mean of 110 and a standard deviation of 15. We want to be on the top 20% of the scores. So, we want to find the mininum x0 such that

Let us calculate the following

that is, we subtract the mean from X and divide it by the standard deviation. So we have that Z is normally distributed with mean 0 and standard deviation 1. So we have, in terms of Z that

Let us call

so now, we want to calculate z0. Using a table for the standard normal distribution we have that

when z0 is approximately 0.84. So we have that

now, we replace that in our previous equation to get

we multiply both sides by 15 to get

Finally, we add 110 on both sides so we get

so the minimum score for being on the top 20% is 122.6