Reading Latency: Averages, Percentiles and Fan-out

A dashboard shows the checkout API's average latency as a steady 120 ms, but support tickets say "checkout sometimes hangs for 5+ seconds". A sample of 1,000 requests from one minute shows: 950 requests at ~90 ms, 40 requests at ~400 ms, and 10 requests at ~5,000 ms.

1. Compute the mean, p50, p95 and p99 for that sample. What does each tell you and why did the dashboard hide the problem?
2. The checkout page renders by calling 20 backend services in parallel and waits for all of them. Each backend has p99 = 300 ms. What fraction of page loads will experience at least one backend at or above its p99? What does that imply for the page's own p99?
3. Given the sample above, which observability signals (metrics, logs, traces) would you use in what order to find the cause of the 5 s requests, and what specifically would you look for?