Why would you assume independence?
That's why I underlined that fact. Obviously there's not independence because students in a given class might be extra motivated if that class is in a prep school or if the teacher offered some big prize to everyone who gets a perfect score.[/quote]
So then why post the(incorrect) math?[/quote]
Introducing conservatism into your estimates while clearly stating your assumptions is done all the time in actuarial work, especially when the unknown piece(s) of the equation is going to be a rough estimate at best (such as the correlation between the scores of the students in question due to their shared background). Well done Jamin.
-TGD, FSA 2011, MAAA 2013