An interesting question. If I were to receive such a question in an interview, I would start by clarifying a few things:
- Should I estimate the number of hot dogs sold, or the number of hot dog eaters?
- How is "hot dog eater in NYC" defined?
Once I have those two questions answer, I would start with the NYC population, and apply (some if not all of) the following filters:
- Remove people who cannot eat hot dogs (e.g. new-born babies, terminally-ill elderlies, people under specific health conditions, religious reasons, etc.)
- Filter by age: assumption here is that certain generations are more likely to consume hot dogs.
- Filter by weight: assumption here is that heavier people are more likely to consume hot dogs.
- Filter by district/location: assumption here is that people from certain parts of NYC are more likely to consume hot dogs.
- Filter by nationality: assumption here is that people from certain countries are more likely to consume hot dogs.
Each of these filters apply a certain percentage number to the NYC population, and the result would be my answer to the question. In a real interview, I would probably use only 2-3 of the filters mentioned above, instead of all of them.