The Hospital Bed Question

THE guesstimate question is a usual type of question that you can expect to be asked when interviewing for a position at a consulting firm.

Here is one to test your mettle.

The Hospital Bed Question

The question is this: How many hospital beds are required in New York city to provide for all of its pregnant women? 

You can assume that:

  1. pregnant women stay in hospital for one night only (American hospitals are very expensive); and
  2. hospital beds in New York are used exclusively by New York residents (no sharing).

If you are game to test your skills, then this is what you need to do.

Please respond in the comments below, covering the following in your answer:

  1. set out the steps that you would take to answer the question;
  2. note any additional assumptions that you would make at each step; and
  3. provide a final numerical guesstimate to the question.

To spice things up, I will be happy to send the best answer (as judged by me) a copy of an interesting book by Lawrence Weinstein (nuclear physicist) and John Adam (professor of mathematics). The book is called Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin.

Note that the comments section remains open for 14 days only, so you have a limited time in which to respond…

Happy guesstimating.

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5 Replies to “The Hospital Bed Question”

  1. I’ll take a swing at this….
    1. Determine the number of people living in NY…According to the US Census Bureau….8,175,133
    2. Determine the percentage of NY population who are female….According to US Census Bureau….52.5%
    3. Determine the percent of women population who are child-bearing age (15 to 44)….According to US Census Bureau this is 44.54%
    4. This should bring us to 1,911,632
    5. Assume a constant replacement population for the next generation (meaning the number of women aging out of this range equals the number of women aging into this range)
    6. Assume no major power outages or other disruptions in infrastructure or societal views to pregnancy, teen pregnancy, women in workplace etc.
    7. Assume the top 20% of the women of child bearing age will bear a median 4 children, the bottom 20% will bear a median 1.5 children and the middle 60% will bear a median 2.5 children.
    8. This yields 4,970,825 births over the next 30 years (age range of child bearing women 15 to 44) or averaging 165,694 per year. Assume equally distributed.
    9. Assume there is no seasonalities to births, equally distributed through the year, this means there should be 453…round up 454 beds to handle pregnant women in NY.

  2. You’d need to account for planned deliveries (Cesarean/induced) against emergency/natural. The former allow a degree of ‘moving’ births to match bed availability. The latter will have more peaks/troughs so you’d need more ‘spare’ beds.

    Item 7 estimates seem very high to me. Rather than look at the number of women, I’d have looked at the number of kids in the first year of school and assumed that many born each year.

    There are some figures here
    http://schools.nyc.gov/AboutUs/data/stats/default.htm
    but I don’t know enough about the US education system to turn them into ‘X students/year’. About a million students and if I guess at ten years of schooling we are looking around 100,000 a year.

    Not sure about home births in the US (New York specifically) either. Maybe not a big deal in the city.

  3. You’re right, a declaration of the assumptions regarding planned deliveries versus natural. The reason for not doing so is there is a two week window around these dates (except in extreme emergencies i.e. neonatal).

    You may be correct on the assumption in number 7. Statistically, that group will outperform the other groups in child bearing. without data medians needed to be assumed.

    Here is a link to the New York City Vital Statistics from 1898 to 2007. http://www.nyc.gov/html/doh/downloads/pdf/vs/2007sum.pdf
    You will see since 2002 the rate of growth in births is 0.94%. Assuming that rate continues through 2011, the birth rate may be close to 133,992. My guesstimate was 165,694. This leads me to believe the assumptions in #7 were overstated. It would be interesting to know the actual medians.

    Thanks for the input. Sharpening the edge is always a good idea.

    Jim

  4. Jim,

    Nice effort with your guesstimate.

    Not sure if you are planning to interview with consulting firms, but if so here are two comments which should help:

    1. you can use round numbers. E.g. your estimate for the population of NYC could be simply 8,000,000. This will make the calculation much easier;
    2. in an interview you would not have access to the US Cencus Bureau. How would you estimate your point 3 without referring to the US Cencus Bureau?

    ~ Tom

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