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

No annotations are provided, so the description carries the full burden. It does disclose a real behavioral trait: the paywall/trial model ('5 free trial calls per signed wallet'), which tells the agent a signed wallet is required and a quota applies. It says nothing about the return format, error behavior for invalid sd (e.g. sd<=0), or whether inputs are parsed as floats.

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?

A single front-loaded sentence that states the result and the inputs with no filler; only the trailing emoji/promo clause is non-essential.

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 math tool with no output schema, no annotations, and three completely undocumented string parameters, the description should at least specify input format and the standard-normal alternative. As written, an agent cannot reliably construct the call or know what shape the answer takes.

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 0% and all three parameters are untyped strings with no descriptions. The prose names x, mean and standard deviation, which gives basic semantics and expands the 'sd' abbreviation, but it adds no format, range, or default information, so it only partially compensates for the coverage gap.

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 states a specific verb and resource ('Returns the normal cumulative distribution at x') plus the two shape parameters, so an agent knows exactly what computation happens. It does not, however, distinguish itself from close siblings like x402-standard-normal-cdf or x402-normal-pdf, which an agent could easily confuse with this one.

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 versus x402-standard-normal-cdf (the mean=0, sd=1 case), x402-normal-pdf, or x402-normal-quantile. The only extra text is a promotional free-trial note, which is not usage guidance.

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