Today was a day of bad communication.
First off, I was in a meeting that was unidirectional in terms of information flow. We hit all the points in question, and at the end of the meeting, I screwed up. I asked a discussion question in a non-discussion oriented forum. The meeting went downhill directly after that. Looking back on it, I basically hijacked the meeting by altering the format of the meeting.
In the meeting, I had an idea, and like a fool I spoke up without thinking about it and asking others what they thought. So naturally, I ran into a brick wall of antagonism in front of a group. Presenting an unknown is really hard, so why did I go that route, instead of prepping everyone and making sure I wasn't off base? Because I'm still learning this stuff, that's why.
Third, teaching is really hard, and I just always seem to make my teachers' lives harder than they have to be. We're going over homework, and the prof arrived at a different answer than I did. So, I questioned it. Unfortunately, this put the prof on the defensive, which makes information exchange harder. I tried explaining my viewpoint twice and just got told it was wrong and that I need to do it a certain way. I find it hard to believe that I'm in graduate school and this is happening.
For the curious, the problem was: Given 60 students taking an exam, the mean time to completion of the exam is 80minutes, and the standard deviation is 10minutes. How many students can be expected to not complete the exam in 90minutes? You end up with 9.522 students being expected to not complete, and this is where my question came in. The answer is 10 students.
I reasoned that at most you will have 9.522 students fail, so you only really have 9 students failing. To round up to 10 students would be to inflate the number of incompletions by eating into the number of completions.
Later on, I reasoned that this argument leads to a broken situation. Say we apply the same argument to answer how many completions will there be? We'd get 50 completions. But we know that completions plus incompletions must total to 60, so our line of reasoning is incorrect. Because we're working with discrete values, we need to round our numbers off consistently in order to preserve basic integer math. In doing so, we'd like to also recognize the fact that over a million trials, 522,000 instances of the qudent (a student in quantum superposition, naturally ;) would incomplete, so we assign a value to the discrete amount according to its continuous bias.