SooTool

probability.lognormal_cdf

Read-onlyIdempotent

Calculates the lognormal cumulative distribution probability P(X ≤ x) from x and the mean and standard deviation of ln X, returning a rounded numeric result.

Instructions

로그정규분포의 누적확률 P(X ≤ x) = Φ((ln x - μ)/σ)를 구한다. x 는 양수, mu 와 sigma 는 ln X 의 평균과 표준편차(sigma 는 양수, 기본 0 과 1)이며 scipy float64 계산 후 유효숫자 10자리로 반올림한 문자열을 반환한다. mu 와 sigma 에 X 자체의 통계량을 넣으면 틀린다.

Input Schema

Name	Required	Default
`x`	Yes
`mu`	No	0
`sigma`	No	1

Output Schema

Name	Required	Description
`_meta`	No	서버가 붙이는 영수증(integrity), 엔진, 힌트
`trace`	Yes	계산 근거(tool, formula, inputs, steps, output)
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.3.0Oct 29, 2026

TDQS

A4.3/5.0

Behavior4/5

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

Annotations already establish read-only, deterministic, closed-world behavior, and the description adds real value on top: the computation is done in scipy float64 and the result is rounded to 10 significant digits and returned as a string. It does not say what happens on invalid input (x ≤ 0, sigma ≤ 0), which is the main remaining behavioral gap.

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

Conciseness4/5

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

Three dense sentences: purpose + formula first, then argument constraints and return format, then the common misuse warning. No filler, though the misuse warning and the parameter constraints could be merged.

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

Completeness4/5

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

An output schema exists, and the description still usefully notes the string/10-significant-digit return convention. Combined with the formula and parameter constraints this is sufficient to call the tool correctly; only edge-case/error behavior is missing.

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

Parameters4/5

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

Schema description coverage is 0% (parameters carry only titles and defaults), so the description must carry the load — and it does, defining x as positive and mu/sigma as the mean and SD of ln X with stated defaults 0 and 1. The one unstated case is the failure behavior for out-of-range x or sigma.

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

Purpose5/5

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

States a specific verb and resource (cumulative probability of the lognormal distribution) and gives the exact formula P(X ≤ x) = Φ((ln x - μ)/σ), which unambiguously separates it from lognormal_pdf and lognormal_ppf in the sibling set.

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

Usage Guidelines4/5

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

Gives clear domain preconditions (x must be positive; sigma must be positive) and a strong usage warning that mu/sigma are the log-scale mean and SD, not the raw X statistics. It does not explicitly name PDF/PPF as alternatives, so it stops short of full routing guidance.

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

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