“like probability theory and continuous probability distribution”
You have no idea of what you say in relation to Public Opinion Polling.
A small population state does not make a small opinion poll any more accurate.
The numerical weight of those polled is constant and equals a normal distribution error range + or - a certain percentage.
Don’t use big words if you don’t have a clue as to what you are talking about.
Who said it did? I surely didn't.
What I did say is that a sample size of 400 isn't any less accurate than most national polls with respect to margin of error.