Choose group-call participant cap via distribution
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
You must decide whether to cap the maximum participants in a Group Call. Given the historical distribution of inferred desired group sizes in the last 28 days: size:count = 3:800, 4:500, 5:260, 6:160, 7:120, 8:80, 9:20, 10:10 (total=1,950). Quality-of-service (QoS) model: MOS(size) = 4.5 − 0.1 × (size − 2). Business requirement: at least 95% of calls must achieve MOS ≥ 4.0. Tasks: (a) Plot and label axes—what are x-axis and y-axis? (b) Compute the 95th percentile of the size distribution. (c) Verify whether that percentile satisfies the MOS constraint; if not, choose the largest integer cap that does, and quantify the coverage fraction under that cap. (d) Discuss trade-offs (QoS vs reach) and propose one adaptive policy (e.g., dynamic cap based on device/network conditions) and one statistical monitoring rule to revisit the cap over time.
Overview: This question evaluates distribution analysis, percentile calculation, performance modeling via a MOS function, trade-off quantification between quality-of-service and user reach, and the design of adaptive policies and monitoring rules—skills relevant to product-focused data science.
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