here is my question. I have a normal distribution with known mean and variance.
Say the mean is 3 and the Var. is 2.
what is the probability that the random variable is taking value 2.9?
If I plug in the value 2.9 into the formula for normal distribution, I think I only get the density value at the point 2.9, not the probability.
I understand for continuous random variable, the prob. at individual point is zero.
In my problem, I just want to know what's the prob. that the random variable is going to take value 2.9?
How can I do it?
Should I calculate the this prob. using a small interval that includes 2.9, for example, I calculate the probability when the random variable falls into the interval [2.85, 2.95]? And using this probability as my answer?
Thank you John