I've searched the web and these forums but couldn't find a subject that resembled my problem. If I missed something then I'd like to apologize upfront.

My problem is this. I have a given probability

*p*, given by an outside agency and the number of successes

*n*from an owned datasource. I'm interested in the population total

*N*and the confidence interval of

*N*.

Background: I know how many passengers there are for a specific bus agency using 2013 data (as in: I have the (micro)data from that specific company). Assumption: this is my

*n*. I also know from transportation figures (from an outside agency) that this specific bus company had a market share (as measured in passengers) of 30% in 2013. Assumption: this is my

*p*. This assumption brings with it certain other assumptions, that is fine.

So now the question is: how many passengers were there in total (assuming this can not be taken from the transportation figures)? ie. what is

*N*and what is the 95% confidence interval surrounding

*N*?

So my questions are:

1) Can I just use the relation:

*p*=

*n*/

*N*, therefore the point estimat for

*N*is:

*N*=

*n*/

*p*? I'd assume so.

2) Can I just use the Clopper-Pearson interval to calculate an interval for

*p*, then using that to get to an interval for

*N*?

3) Suppose the 95% lowerbound for

*p*=plb. Is the 95% lower bound for

*N*then

*n*/plb? Same logic for the 95% upper bound.

4) When calculating the Clopper-Pearson interval, can I just use:

*n*=

*n*,

*p*=

*p*,

*N*=

*n*/

*p*?

5) If any of the answers to my questions 2-4 is 'No', then what is the correct approach?

I realize that using this approach,

*N*is not necessarily an integer. Is that problematic?

Thanks for any help,

Jasper