Integration limits for continuous probability distribution to model distrete output boundaries

by jens0r   Last Updated May 01, 2017 14:19 PM

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?

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