Assume that I have a population of size $N$ with an attribute which is a continuous variable. Let's say these are people and the attribute is their height. I want to find the $90\%$ quantile of that population. But instead of calculating it from the entire population, I'd like to estimate it from a sample I take.
I think that taking the $90\%$ quantile of the sample will be the best estimator for the $90\%$ quantile of the population (correct me if I am wrong). How good is this estimation though? In other words what is the probability that the true quantile is at most $x\%$ away from the estimation? Or conversely, what should the sample size be so I can achieve a certain confidence in my estimation (e.g., I am within $10\%$ of the true value with probability $0.99$)