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Equation 9 · Building a Production-Grade MCP Server

What does this equation mean?

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

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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nn

Symbol n

n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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z2z^{2}

Symbol z^2

The square of z: multiply z by itself.

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pp

Symbol p

the some true success probability.

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e2e^{2}

Symbol e^2

The square of e: multiply e by itself.

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fraction

fraction

Divide the expression above the line by the one below it.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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z2 p(1−p)z^{2}\, p(1-p)

Numerator: z^2 p(1-p)

The complete quantity above the fraction bar.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

What the article says around this equation

​ . 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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Sources cited in the article section

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