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Equation 9 · Part 5 · Building a Production-Grade MCP Server

fraction

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

What this part means

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

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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 fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the article section

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