I don't have a mathematical background so I apologise if this seems a bit simple for this forum, I'm not sure if this problem has a name in maths circles or is just too simple but I don't know the technical terms to search under.
I have a population of 3.2 billion and I want to measure something in X percent. I can sample up to half of the population at any one time. How would I calculate how many samples I would need to take to have measured X percent of my population. I presume there will be a mean number of samples I would have to measure and a standard deviation associated with this mean. I imagine if I was to plot n-samples, vs % of population sampled that it would converge towards 1.
I'm sure this is a simple problem for quant-people? Many thanks