Given a binomial distribution (p and n are known), does it make sense to construct a confidence interval around expected mean?
I guess my question is more about confidence intervals in general: usually we have a sample and estimate a population parameter based on that sample. In this case each (other) sample might lead to a different estimation and thus we use the confidence interval (and level) to communicate the uncertainty.
In my case, however, I do not have a sample to estimate the mean value from. I have concrete distribution parameters (p and n) and I "predict" that (intuitively) in most cases there will be p*n successful outcomes.
I am not sure how I can apply confidence intervals here. Will my confidence interval be simply defined by the area under the distribution function, which is equal to the confidence level?
Please note that I am *not* estimating the value of 'p' from a sample (this is the topic that would be most probably brought up if you search for "binomial distribution confidence interval" on the web).