Latency distribution of N parallel tasks

A common thing in any system is running a bunch of similar tasks. For example, to serve a request we need to read a number of enries from a database (so the “task” in this case is a database read). We typically have an idea how latency for a single task looks like. Being good engineers and caring about observability we likely measure average latency $ T_{avg} $ and things like p95/p99 quantiles and standard deviation $\sigma$ (maybe we even have opentracing instrumentation to measure those with).