Determing sample size

#1
Any help appreciated!!!

What is the formula I need to use if I want to determine sample size for an unknown population (the number of workers) when you are going to a known number of facilities? This is the information I know right now:
- I will need a stratified sample because there are several different types of facilities that we can go to (131 of type a, 1578 of type b, 600 of type c, and 1662 of type d).
- the number of workers in the total population is unknown, hence the reason for the survey. we can assume that the number of workers is randomly distributed in each of the facility types.

I want to calculate the minimum amount of facilities that I would have to visit to get a good idea of the number of total workers in all facilities, with various margins of error.

No other information is known. What is the best way to go about doing this?
 
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