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n\sqrt{n}

Why this formula appears here

There is a statistical floor underneath all of this worth making explicit, because it exposes an assumption a five-run smoke test quietly violates. A model’s behaviour on a given prompt is not deterministic across runs, so a single trial is one draw from a Bernoulli process with some true success probability p , and the uncertainty in an observed rate p^\hat{p} from n independent trials shrinks only as n\sqrt{n} . To bound that uncertainty to a half-width e at a chosen confidence level z , the standard requirement is

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nn

Symbol n

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n\sqrt{n}

Equation 6 · AI Infrastructure

Building a Production-Grade MCP Server

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

There is a statistical floor underneath all of this worth making explicit, because it exposes an assumption a five-run smoke test quietly violates. A model’s behaviour on a given prompt is not deterministic across runs, so a single trial is one draw from a Bernoulli process with some true success probability p , and the uncertainty in an observed rate p^\hat{p} from n independent trials shrinks only as n\sqrt{n} . To bound that uncertainty to a half-width e at a chosen confidence level z , the standard requirement is

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