I'm doing some education research and would love some help! I'm guessing I need to learn about Z-statistics, but I'm just a beginner at stats....

We're looking at the scores of students across a country. The average score is 0. It's pretty much a normal distribution, will students doing less well having a negative score. Most scores range from -1 to +1, the standard deviation is -0.36.

I have a group of a particular kind of students, let's call them SS, who have an average mean nationally of -0.47 (and a similar standard deviation to the main population). They aren't doing so well. In comparison, the non-SS students have a mean score of 0.19.

What is the probability that if I have a school with a total of say 100 students, and say X of them are SS, that the SS students do better (have a higher mean) than the non-SS students? Even though on average across the country, they do 0.47 worse?

Thanks!