stats_normal-distribution

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

Annotations already indicate readOnlyHint=true and idempotentHint=true, so no destructive behavior. The description adds value by listing the return values (CDF probability, PDF density, z-score, quantile value, confidence interval bounds), which is beyond what annotations provide.

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?

The description is three sentences, front-loaded with purpose, and every sentence adds value. No redundant or filler content.

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?

Despite having no output schema, the description explicitly lists all possible return values and covers the three modes of operation. It also explains parameter relationships, making the tool fully understandable for its moderate complexity.

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 coverage is 100% with descriptions for all 5 parameters. The description adds contextual guidance on when to use each parameter (e.g., 'Provide x (for CDF/PDF), p (for quantile)'), enhancing the schema definitions.

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?

The description explicitly states 'Normal distribution: CDF, PDF, quantile, and confidence intervals' and details the specific computations, distinguishing it from sibling tools like stats_distribution-fit which focus on fitting rather than direct computation.

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?

The description clearly states 'Use when computing normal distribution CDF, PDF, quantiles, or confidence intervals' and maps parameters to use cases (x for CDF/PDF, p for quantile, confidence_level for interval). It lacks explicit exclusions or direct alternatives, but the context is sufficient.

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