probability.normal_ppf

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

Annotations already cover safety (readOnly, idempotent, closed-world), and the description adds real context beyond them: scipy float64 computation, a return value rounded to 10 significant digits as a string, and a documented error case for boundary q. It stops short of describing precision caveats or failure behavior beyond the q boundary.

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?

Three sentences: formula first, then parameter constraints and return format, then edge cases and the critical-value tip. Every sentence carries information an agent needs, with no filler.

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 scalar function with an output schema available, this is complete: domain constraints, defaults, error condition, return type and rounding, and the practical α/2 idiom are all present.

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%, so the description must carry the load, and it does: q is a probability in the open interval (0,1), mu defaults to 0, sigma is a positive standard deviation defaulting to 1. It does not explain why all three are typed as strings (presumably decimal-precision inputs), which is the one remaining ambiguity.

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 names the specific operation and gives the exact formula (x = μ + σΦ⁻¹(q)), which unambiguously distinguishes it from sibling probability.normal_cdf and probability.normal_pdf. An agent can tell what it computes without opening the schema.

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?

It states the valid domain (q strictly between 0 and 1) and the error condition (q = 0 or 1), plus a concrete usage tip: for two-sided critical values pass 1-α/2 as q. It does not explicitly route between this and the CDF/PDF siblings, but the guidance is otherwise clear.

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