For a future monitoring program on small water bodies we want to calculate the sample size. The bodies of water are so small that their number easily exceeds 100.000 in the monitoring area and therefore we assume the sample population to be infinite. With the future monitoring data we want to be able to assess whether 99% of the water bodies are unaffected by pollutants. From former monitoring programs we know that 99% are unaffected.
My approach calculating the sample size:
P = 0.01 # sample proportion e = 0.01 # margin of error level = 0.95 # confidence level N = Inf # infinite population q = qnorm((1 + level)/2) n = P * (1 - P) / (e^2/q^2 + P * (1 - P)/N) n  380.3044
Using this formula I get 380 samples. However I read several times that for a sample proportion close to 0 or 1 using the approach of the Normal Approximation is not valid.
1) What could I use instead?
2) changing the margin of error only a little bit has considerable influence on the number of samples. E.g. for
e = 0.02 I already get an
n of 95.07. Is this the result of using a close to 0 sample proportion?