Choose group-call participant cap via distribution
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.
Group Call Cap Decision: QoS vs Reach
You are deciding whether to cap the maximum number of participants in a group call. You have the past 28-day distribution of inferred desired group sizes (size: count):
- 3: 800
- 4: 500
- 5: 260
- 6: 160
- 7: 120
- 8: 80
- 9: 20
- 10: 10 Total calls = 1,950.
Quality-of-service (QoS) model:
- MOS(size) = 4.5 − 0.1 × (size − 2) = 4.7 − 0.1 × size
Business requirement:
- At least 95% of calls must achieve MOS ≥ 4.0.
Tasks: (a) Describe the plot you would make and label the axes. (b) Compute the 95th percentile of the size distribution. (c) Check whether that percentile meets the MOS constraint; if not, choose the largest integer cap that does. Quantify the coverage fraction (share of calls with desired size ≤ cap). (d) Discuss QoS–reach trade-offs. Propose one adaptive policy (e.g., dynamic cap based on device/network conditions) and one statistical monitoring rule to revisit the cap over time.
Solution
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