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Equation 9 · Part 2 · Building a Production-Grade MCP Server

Symbol z^2

n  ≥  z2 p(1−p)e2,n \;\geq\; \frac{z^{2}\, p(1-p)}{e^{2}},
z2z^{2}

What this part means

The square of z: multiply z by itself.

Its job in the formula

z2z^2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

See this notation across published equations →

Sources cited in the article section

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