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

No annotations are provided, so the description carries the full burden of behavioral disclosure, and it discloses nothing: no mention of what the return value is, whether it is an inverse-CDF lookup, precision, or domain limits on p.

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?

It is short, but only because it is under-specified rather than concise — the second half of the sentence repeats the first half and adds no information.

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 one-parameter math utility the bar is low, but with no annotations and no output schema the description should at minimum state what is computed from p and what the result represents. It leaves everything to be inferred from the name.

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 100% for the single parameter, so the baseline of 3 applies even though the description adds no parameter meaning. The schema's own description ('P to process') is weak, but the description contributes nothing extra either way.

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 is a verbatim repetition of the tool name ('Normal Quantile: Normal Quantile'), giving no verb and no explanation of what computing a normal quantile entails. An agent can infer the resource from the name but gets nothing beyond it, and no differentiation from siblings like x402-normal-cdf or x402-normal-pdf.

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?

There is no guidance on when to use this tool versus the many related statistical siblings (x402-normal-cdf, x402-normal-pdf, x402-standard-normal-cdf, x402-zscore). No context, no exclusions, no prerequisites.

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