normal_distribution

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. It clearly identifies a pure mathematical computation, implying no side effects, but does not state that explicitly and is ambiguous about whether all three outputs (PDF, CDF, percentile) are returned together or selected elsewhere. For a stateless calculation tool this is adequate but not rich.

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 with zero wasted words. The verb and resource come first, followed by the specific outputs, which is exactly what an agent needs to scan quickly.

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?

The low-complexity math operation and fully documented schema make the definition workable. However, with no output schema and no description of return format or whether all three quantities are returned, there is a minor but real gap for an agent that needs to know what to expect from the call.

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 schema already documents x, mean, and stddev completely, including defaults and the positivity constraint on stddev. The description adds only the phrase 'for a given value' and does not enrich parameter meaning beyond the schema, matching the baseline for high coverage.

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 ('Calculate'), a specific resource ('normal (Gaussian) distribution'), and the exact operations (PDF, CDF, percentile) for a given value. This distinguishes it from sibling distribution tools like binomial_probability and poisson_probability, as well as generic percentile_calc.

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?

Provides no explicit guidance on when to choose this tool over alternatives, no prerequisites, and no exclusions. The phrase 'for a given value' implies context but gives no comparative or conditional guidance.

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