Assuming I have a continuous probability distribution for some quantity $x$, let's say the grade of a student. I obtained this probability distribution by taking a regression output $x_0$ and moddeling a normal distribution with mean $x_0$ around it.
The acutal grade is discrete in it's values. My question is: how do I get the probability that the grade is bigger than a certain values?
If I'm interested in, let's say, grades bigger or equal than 4 (4,5,6,...) I would have taken the integration limits from 3.5 to infinity, is that correct?
Or is that modeling approach flawed and I should model a discrete probability distribution in the first place?