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

No annotations exist, so the description carries the full burden. It does disclose the input domain constraint (probability strictly between 0 and 1) and a payment/rate-limit trait ('5 free trial calls per signed wallet'), which is genuine behavioral context. However, it says nothing about whether this is the standard normal or a parameterized one (only p is accepted), nor about edge behavior near 0 and 1.

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?

One front-loaded sentence that leads with the action and the resource. The trailing trial-call promo is marginally useful context rather than padding, though it dilutes an otherwise tight sentence.

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 single-parameter math utility with no output schema, the description covers purpose and the input domain but leaves the return value (a z-score/quantile) and the standard-vs-parameterized normal question unstated. It is adequate but not complete enough to call blind.

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 0% and the lone parameter is the uninformative name 'p'. The description partially compensates by defining p semantically as a probability strictly between 0 and 1, but it omits the expected format (the schema types it as a string, presumably a decimal) and gives no bounds-error guidance.

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?

States a specific verb and resource: 'Returns the normal quantile for a probability'. That distinguishes it meaningfully from siblings like x402-normal-cdf and x402-normal-pdf, which are the inverse direction. It stops short of naming those siblings explicitly, so the agent must infer the pairing.

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?

Usage is implied by the input constraint 'strictly between 0 and 1', which tells the agent the valid domain. There is no explicit when-to-use statement or routing to alternatives such as normal-cdf for the opposite direction, so the agent must reason about which of the several normal-distribution siblings to pick.

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