# How many dentists are there in New York?

### Product Management Interview Question: Guess estimate the total number of dentists in New York

In this product management interview question, the interviewer is assessing your ability to provide quick estimates related to a product. The estimation could be about revenue, the number of users, or something else. Why is the interviewer asking you to do this? Because as a product manager you may need to estimate the size of a new market or revenue, or any other business opportunity, to convince stakeholders of a new idea. Therefore, this is an essential skill.

The interviewer is evaluating you on the following:

Are you methodical and articulate when explaining your estimation approach?

Is the interviewer able to follow you when you make calculations?

Can you make calculations quickly?

Do you explain your assumptions convincingly?

The key to answering estimation questions is to separate the “how-to” from the calculations. Separating operations from calculations prevents the interviewer and you from getting lost in calculations and losing track of what you are calculating. An estimation tree does this. Using an estimation tree allows you to explain your logic behind the operations first, to then focus solely on calculations.

### Here is how to structure the answer:

**Ask clarifying questions.**Clarifying eliminates any ambiguity of what should include in your calculations.**Make an equation.**Consider edge cases or alternate sources of data and writing any facts that you know helps with calculations.**Break down the equation into components.**Write your assumptions next to the components. Doing this reminds you to explain the assumptions clearly to the interviewer.**Do the math.**Calculate the result of each component and compute the result.**Do a sanity check.**Do your results make sense? If not, recheck your equation, assumptions, and arithmetic.

To help you with your Product Manager interview preparations, we have compiled a complete list of the most asked **Product Management Interview** **Questions** and **Answers at companies like Facebook, Google, Amazon, Microsoft, Netflix, etc. answered by PMs at FAANG.**

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**1. Ask Clarifying Questions**

Q) Assuming this is for New York City and Not New York state.

*A) Yes.*Q) We are talking about people who are practicing dentistry either part-time (4 hrs/day) or full-time (8hrs/day) in NYC.

*Not estimating dentists who are not doing work, retired, or simply do it occasionally or dentistry staff.**A) Yes*

### 2. Approach:

I want to find out how many patients can a dentist serve. This will help me calculate the total number of dentists serving 8M people in NYC.

To estimate the number of patients a dentist can support, I need to estimate the number of hours a dentist spends on a patient. I typically visit my dentist twice a year and each visit takes 30 mins.

In other words, I spend about 2x30min = **60 mins per year** with a dentist.

Now, it’s important to remember that the average time per year per patient varies depending on the age group and insurance status. Also, some people may not visit a dentist every year.

### 3. Make an Equation:

Number of Dentists in New York =

The eligible population who visit dentists / Number of patients per dentists

**4. Breakdown of Equation: **

Total Population of New York City = 8 million.

Assuming people are evenly distributed between 0 to 80, meaning each age group population is 8 Million / 80 = **100K.**

**1. 5-20 year olds:**

40%. Hence, Visit = 60% of 100k =**Do not visit -****60K.**– 20% of population in this remaining group = 20% x 15 years x 60K per year = 180K visit 20 mins per year.**Visit with no insurance**– 80% of the population in this remaining group = 80% x 15 years x 60K per year = 720 K visits 40 mins per year.**Visit with insurance**

**2. 20-50 year olds:**

30%. Hence, Visit = 70% of 100k =**Do not visit -****70K.**– 20% of population in this group = 20% x 30 years x 70K per year = 420K visit 30 mins per year.**no insurance**– 80% of population in this group = 80% x 30 years x 70K per year = 1.6 million visit 60 mins per year.**with insurance**

**3. 50-80 year olds:**

30%. Hence, Visits = 70% of 100k =**Do not visit -****70K.**– 20% of population in this group = 20% x 30 years x 70K per year = 420K visit 40 mins per year.**no insurance**– 80% of population in this group = 80% x 30 years x 70K per year = 1.6 million visit 80 mins per year.**with insurance**