You still do not show HOW you get your numeric results. Those results are wrong. How in the world can we help correct your method of computation if you do not show us exactly what you have done?ok let me formulate problem for you. Suppose we have 1 million parts which have 1% defective parts. so there are 10000 defective parts in 1 million parts. Now If i add 10% more parts to these 1 million parts with no defects added, total I have 1100000 parts and value of success for finding defects parts, p is 10000/1100000 from these 1100000 parts. I want to calculate probability of finding at most 5000 defective parts from these 1100000 parts. I am calculating mean and standard deviation because I m using normal approximation, Besides you can see Dr Phil earlier replies to understand the need of mean and standard deviation calculation. My issue is if I am calculating mean and standard deviation for 10% added parts (total )1100000 parts, 20%(1200000), 30%(1300000),40%(1400000) till 90% added parts (1900000 parts) value of mean and standard deviation is same. I cant understand where the problem is?
When you first presented your problem, it involved a population of constant size and changing but known sizes for the sample. Now the problem seems to involve a changing size of population and an unknown but apparently constant size for the sample. So which problem is it? If it is the second problem, what is the size of the sample? In either problem, are you sampling with or without replacement? If you are sampling without replacement, the binomial distribution is at best an approximation because the probability of choosing a defective changes as your sample is selected. Formally, you have an "urn" problem, a classic problem in probability theory. If we could ever be sure that we knew what the problem is, someone here could tell you what to use as a computational approximation for the exact formula used to solve the urn problem. That approximation may or may not be the binomial distribution.
Now without doing any computations at all, I can tell you the general shape of your curves.
If the question involves a fixed size of the population and a variable size of the sample, the probability that at most 5000 are defective is 100% if the sample is small enough and is 0% if the sample is large enough. Consequently, your probabilities should not be rising as sample size increases. If your sample size is 1000, what is the probability that no more than 5000 are defective? Obviously, it is 100%. If your sample size is the population minus 1 and you have 10,000 defectives in the population, your sample will contain either 9,999 or 10,000 defectives so the probability that it will contain at most 5,000 defectives is zero.
If the question involves a changing size of the population and a constant size of the sample, your probabilities that your sample of fixed size will include at most 5000 defectives will increase (unless it already is 100%) as the population increases.