Here is one way of doing it
# Hospitals = (US Population x % who get sick once per year x % who visit hospital) / (average hospital capacity per year x average hospital utilization rate %)
US population x % who get sick x % who visit hospital: You can segment this out by age bracket and assign higher sickness % and hospital visits % to the more elderly age brackets.
The key assumption here is patients only visit hospitals once. You can add some more assumptions for multiple visits if you like
Average hospital capacity x utilization rate: Assume each hospital has 150 beds, average stay time per patient is 2 weeks, average utilization is 80%. Hence, the hospital can service 3000 patients per year (150 x 25 x 80%)
Putting it all together: Just to illustrate the logic, if US population is 300m, 20% get sick once per year, 10% of that goes to hospital. Then there are 6m hospital visits per year (300m x 20% x 10%).Then each hospital can service 3000 patients.
That then gives you 2000 hospitals.
A quick sense check - 2000 hospitals implies 1 hospital every 150,000 people. I live in San Francisco - which has about 800,000 people and about 5-10 hospitals. So that is about in the ball bark. It might be a bit low because we did not count for people who visit hospitals more than once per year.
Hope that helps!
You could approach this from the supply side or demand side.
For the demand side:
1.) Determine on average, how many patients per hospital in a given year (i.e the market just for one hospital).
2.) Determine the size of the us population
3.) Divide the US population by the number of patients per hospital to get total hospitals in the US
There are of course several other ways to do this, most of which are more complex- but this is a basic framework you could use.
2 solid answers already; here's a 3rd approach using 'baby math', which you can even use at the end of a more complex estimation approach to confirm the result makes directional sense
- You know how many hospitals are in a small area you come from (100k people live here, 2 hospitals). This suggests 1 hospital per 50k inhabitants
- Let us further assume the local population needs medical care at roughly the same rate than the average in the country, and our hospitals are roughly the average size
- There are 300M people in the US
- I would therefore expect there to be ~6,000 hospitals in the US
(1) always more than 1 way to skin the cat (poor cat);
(2) some cases are all about the market sizing so it makes sense to run a very detailed scenario, but others only require a very high level market sizing to time is of the essense;
(3) last but not least, you know the estimation will be wrong, and your interviewer doesn't know the right answer either. Better be roughly right than precisely wrong.