What is the minimum population size from which one can draw a random sample and have a 95% confidence level?

I will rephrase your problem slightly.

If we take n samples from a population that has the normal distribution with mean MU and standard deviation SIGMA, and calculate the sample mean XBAR from our sample, then what is the value for n so that the probability is 95% that XBAR will be close to MU?

(XBAR - MU)/(SIGMA/SQUAREROOT(n)) = 1.96

SQUAREROOT(n) = 1.96SIGMA/.95

n = (1.96SIGMA/.95)^2