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stats_normal-distribution

Read-onlyIdempotent

Calculate cumulative probabilities, density values, quantiles and confidence intervals for normal distributions using mean and standard deviation parameters.

Instructions

Normal distribution: CDF, PDF, quantile, and confidence intervals.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xNoValue to compute CDF/PDF for
pNoProbability for inverse CDF (quantile)
meanNoDistribution mean
stdNoDistribution standard deviation
confidence_levelNoConfidence level for interval (e.g. 0.95)
Behavior2/5

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

The annotations comprehensively cover safety profiles (readOnlyHint, destructiveHint, idempotentHint), so the description does not need to address those. However, the description fails to disclose return value formats, computational behavior, or the mutually exclusive relationship between the x and p parameters despite the absence of an output schema.

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?

The description consists of a single 7-word fragment that immediately states the supported operations without redundancy. While appropriately brief for a mathematical utility, the extreme brevity sacrifices opportunity to provide usage guidance or behavioral context that would assist agent invocation.

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

Completeness2/5

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

Given the absence of an output schema and the tool's multiple operational modes (CDF, PDF, quantile, confidence intervals), the description inadequately explains what values are returned or how the parameters interact. The description should specify that x and p are mutually exclusive inputs for different calculation directions and describe the return structure.

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

Parameters3/5

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

With 100% schema description coverage, the structured schema already documents each parameter's purpose (e.g., 'Value to compute CDF/PDF for', 'Probability for inverse CDF'). The description lists the operations available but adds no semantic meaning regarding parameter relationships or constraints beyond what the schema provides, warranting the baseline score.

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

Purpose4/5

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

The description identifies specific statistical operations (CDF, PDF, quantile, confidence intervals) performed on the normal distribution resource, using precise terminology. While it clearly indicates the tool's functionality, it does not explicitly differentiate from sibling statistical tools like stats_sharpe-ratio or stats_realized-volatility regarding when to prefer this specific distribution analysis.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives, nor does it clarify which parameters to use for which calculation type (e.g., using x for CDF/PDF versus p for quantile). There is no mention of prerequisites such as requiring exactly one of x or p to be provided, or that confidence_level operates independently.

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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