Here is the problem: Average mark in a class test is 11±3. What is the probability (P) for a student to get 4 marks at 0.05 Significance Level?
I am not interested to calculate P for a student to get 4 marks or lesser (which is a cumulative function). I want to calculate the exact Probability for a student to get 4 marks. Could you please help?
Thanks!
Obviously, the true number of marks isn't Normally distributed, but it could be modelled as the integer closest to a Normal variable, so you want $$P(3.5\le X\le 4.5|X\sim N(11,\,9)).$$Which is just as well, because a genuinely Normal variable has zero probability of being exactly equal to any value you name.