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

No annotations are provided, so the description carries the full behavioral burden, and it discloses nothing: no input domain (standard normal vs. general normal), no precision or range behavior, no return format, no edge-case handling for extreme x. For a computation tool with zero annotation coverage this is a complete gap.

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 the brevity comes from duplication rather than economy — the single sentence repeats the title back with a colon. No sentence earns its place because no information is conveyed.

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 tool with no annotations and no output schema, the description should at minimum state that it returns P(Z <= x) for a standard normal and that x is a z-score. Neither is present, leaving the agent to infer the entire contract 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%, so the baseline is 3 even though the description adds nothing about the parameter. The only schema text is the unhelpful 'X to process,' but per the rubric the high coverage keeps this at the baseline rather than lower.

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 restatement of the tool name: 'Standard Normal Cdf: Standard Normal Cdf.' It contains no verb, no stated output (CDF value), and no differentiation from close siblings such as x402-normal-cdf, x402-normal-pdf, or x402-normal-quantile. An agent only knows the purpose because the name itself is a mathematical term.

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 when-to-use guidance, no mention of when to prefer x402-normal-cdf (which appears to be the same function) or x402-normal-quantile, and no statement that the input is expected to be a z-score. Nothing in the text routes the agent to this tool over alternatives.

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