Estimate how many houses could be purchased with the total amount that people in the United States spend on Netflix subscriptions in one year. You start with no reference data — build the estimate from quantities you can reason about, and be explicit about every assumption. This is a Fermi-estimation question from a quantitative interview round. The interviewer cares less about the final number than about your decomposition, your calibration, and how you update when given new information. ### Constraints & Assumptions - "Spending on Netflix" means consumer subscription payments by US subscribers over one calendar year (ignore advertising revenue and corporate accounts). - "Houses" means typical US homes at the national median price; assume the purchases are at market price with no bulk discount. - No external data sources: all inputs must be common-knowledge magnitudes you estimate and justify on the spot. - A 90% interval means you would accept a bet at 9-to-1 odds that the true value falls inside it. ### Clarifying Questions to Ask - Should I count only direct subscription revenue from US customers, or include advertising and other revenue lines? - Is a "house" the median-priced US home, or homes in a specific market? - Do you want a point estimate first and then the interval, or the interval directly? - How precise should the arithmetic be — order of magnitude, or a defensible point value with clean rounding? ### Part 1 Produce a point estimate for the number of houses, and give an interval that you are 90% confident contains the true answer. ```hint Decompose into estimable factors Annual US Netflix spend $=$ (US subscribers) $\times$ (average monthly price per subscription) $\times$ 12. Divide by the median US home price. Each factor is something you can bound from everyday knowledge. ``` ```hint Intervals for a product Your uncertainty is multiplicative, so work in log space: if the factors are independent and roughly log-normal, the log-variances add, and the 90% interval is the point estimate multiplied and divided by $e^{1.645\,\sigma_{\text{total}}}$. Do not just multiply the three most extreme values together — that overshoots 90%. ``` #### What This Part Should Cover - A clean decomposition into a small number of independently estimable factors. - Explicit per-factor assumptions with plausible ranges, avoiding false precision. - An interval built by propagating multiplicative uncertainty (log-space reasoning), not by ad-hoc widening. - Sanity checks: per-household monthly spend, total spend versus the scale of US consumer spending, and whether the implied number of houses is a sensible fraction of annual US home sales. ### Part 2 You are now told that Netflix has about 81 million US subscribers. Update your point estimate and your 90% interval. Should the interval get wider or narrower, and roughly by how much? ```hint Which uncertainty disappears Your interval width came from several independent sources of uncertainty whose log-variances add. Conditioning on the exact subscriber count removes exactly one of those variance terms — recompute the total. ``` #### What This Part Should Cover - Correctly recomputing the point estimate with the given subscriber figure. - Recognizing that the interval must narrow, because one component of variance is eliminated while the others are unchanged. - Quantifying the reduction approximately (new total log-standard-deviation from the remaining terms). - A calibration check: does 81M fall inside the subscriber range assumed in Part 1, and what would it mean if it did not? ### What a Strong Answer Covers Across both parts: genuine calibration (a 90% interval that is neither timidly wide nor overconfidently narrow); a clear separation between the point estimate and the uncertainty around it; transparent mental arithmetic with clean rounding; and correct Bayesian instincts — new information moves the point estimate within the old interval and shrinks the uncertainty rather than being bolted on ad hoc. ### Follow-up Questions - Make a market on this quantity: what bid and ask would you quote, and how do they relate to your 90% interval? - Of the assumptions that remain after Part 2, which single number would you pay the most to learn exactly, and why (value of information)? - How would the answer change if "houses" meant homes in San Francisco rather than the national median? - If you answered 100 questions like this, how would you test whether your 90% intervals are actually calibrated?