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Equation 3 · Part 2 · A Practitioner's Map of Agent Evaluation Frameworks

Symbol z_α/2

p^  ±  zα/2p^(1−p^)n,\hat p \; \pm \; z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}},
zα/2z_{\alpha/2}

What this part means

z_α/2 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

z_α/2 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…noise sits under a given n , even granting the generous and almost certainly false assumption that every task in the set is an equally difficult coin flip. At the widest plausible spread, p^\hat p = 0.5 , a 95% interval ( zα/2z_{\alpha/2} ≈\approx 1.96 ) works out to roughly ±\pm 13.9 points on a fifty-task set — close to the size of tau-bench’s original airline domain or GAIA’s seventy-five-question Level 3 tier — versus roughly ±\pm 4.4 points on SWE-bench Verified’s five hundred tasks, or ±\pm 5.1 points on OSWorld’s…

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