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 computation semantics, no input expectations, no return behavior. An agent learns only the tool name twice.

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 definition is extremely short, but it is under-specified rather than concise — every bit of it is a redundant repetition of the name, so nothing earns its place and there is no front-loaded intent.

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 three-parameter statistical tool with no annotations and no output schema, the description is entirely inadequate. It leaves the agent unable to tell what is computed, what the parameters mean, or how the result is returned.

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 nominally 100%, so the baseline is 3, but the schema text is pure boilerplate ('X to process', 'Sd to process', 'Mean to process'). Only the parameter names (x, sd, mean) hint that this is a normal-distribution computation; the description adds no additional meaning.

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 'Normal Pdf: Normal Pdf' merely restates the tool name verbatim and states no verb or action. The name alone hints at a normal probability density function, but the definition offers nothing beyond that, and it does not distinguish this from siblings like x402-exponential-pdf, x402-uniform-pdf, or x402-normal-cdf.

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 whatsoever on when to use this tool versus the many other distribution/statistics siblings (x402-normal-cdf, x402-normal-quantile, x402-exponential-pdf). No context, prerequisites, or alternatives are mentioned.

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