probability.binomial_cdf

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover safety (readOnly, idempotent, closed-world), and the description adds substantial non-structured behavior: computation via scipy float64, results rounded to 10 significant digits, and the return value delivered as a string rather than a number. That string-return disclosure is operationally important and appears nowhere in the schema or annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Three sentences, front-loaded with the definition, then constraints, then the boundary-interpretation caveat. No filler; every clause carries either a constraint or a behavioral fact the agent needs.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 3-required-parameter numeric tool with an output schema, this covers everything an agent needs: domain constraints on all inputs, the input encoding for p, the rounding behavior of the result, and the directional semantics that most often cause misuse. Nothing material is left to inference.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must carry all parameter meaning — and it does: k and n are non-negative integers with the k ≤ n constraint, and p is a decimal string in [0, 1]. This is critical because the schema types p as a bare 'string' with no format hint; the description supplies the required encoding.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a precise verb+resource with the exact formula notation: '이항분포의 누적확률 P(X ≤ k; n, p)를 구한다'. This unambiguously distinguishes it from probability.binomial_pmf (mass, not cumulative) and from the other distribution CDF tools in the sibling list.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives concrete interpretation guidance: 'k 회 이상'은 1 - cdf(k-1)로 구해야 하며 cdf(k)는 'k 회 이하'다 — directly resolving the most common off-by-one ambiguity for CDF calls. It does not name binomial_pmf as the alternative for exact-P(X=k) queries, so it stops short of explicit sibling routing.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.