The formula for a 95% confidence interval for proportion is
$\hat{p}\pm 1.96 \sqrt{p(1-p)}$
Suposing a sample of 200, calculating a proportion of 1.8%, the confidence interval is 1.67% - 1.93%. But, what if the population size is about 1 billion? Is this correct? I know that there is a finite population correction factor to small populations, but my thought is about big populations with very different sizes.
The formula can be used even to a a 1 million population also to a 1 billion population?