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Equation 9 · Part 3 · Building a Production-Grade MCP Server

Symbol p

n  ≥  z2 p(1−p)e2,n \;\geq\; \frac{z^{2}\, p(1-p)}{e^{2}},
pp

What this part means

the some true success probability.

Its job in the formula

p occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

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} .

The passage around this formula

​ . To bound that uncertainty to a half-width e at a chosen confidence level z , the standard requirement is n  ≥  z2 p(1−p)e2n \;\geq\; \frac{z^{2}\, p(1-p)}{e^{2}}. which, for a rate near one half and a 95% confidence interval within five percentage points, already calls for several hundred independent trials rather than five or ten. The practical conclusion is not that every team needs a statistics department before shipping a tool; it is that “it passed when I tried it a few times” and “it passes at a known, bounded rate” are different claims, and only a CI-integrated harness run at real scale can make the second one.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.