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

Annotations already declare readOnlyHint=true, destructiveHint=false, and openWorldHint=false, so safety is covered. The description adds the domain validity constraint σ > 0, though that is also stated in the std parameter's schema description, and it says nothing about defaults being applied when parameters are omitted.

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?

Two terse sentences, front-loaded with the operation list, with no filler. The second sentence duplicates a constraint already present in the schema, which is the only wasted payload.

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?

An output schema exists and parameter descriptions are complete, so the description does not need to explain returns. However, it never clarifies which parameters pair with which calculation mode (x/mean/std for pdf, cdf, sf, zscore; z/mean/std for from_z), leaving a real gap for a zero-required-parameter tool.

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 100%, so all five parameters including the calculation enum are already documented, which sets the baseline at 3. The description only restates the operation list, and it uses 'survival' where the enum value is 'sf' and 'x from z' for 'from_z', a naming mismatch that slightly hinders mapping intent to the enum.

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 concrete operations (PDF, CDF, survival, z-score, x from z) of a normal-distribution calculator, so an agent knows exactly what the tool computes. It stops short of contrasting itself with nearby siblings such as calculator_binomial or calculator_probability, but the verb+resource pair is specific enough to be selectable.

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 lists calculable quantities but never states when to choose this tool over calculator_binomial, calculator_probability, or calculator_random_distribution, nor which mode fits a given user intent. An agent must infer routing from the option names alone.

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