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

Annotations already declare readOnly, idempotent, non-destructive, closed-world behavior, so the safety profile needs no restating. The description adds only that output consists of CI lower/upper bounds, which the existing output schema already covers, so there is little behavioral value beyond structured fields.

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?

Front-loaded with the core purpose, then usage, inputs, and output in compact order with no filler sentences. The trailing cross-reference to list_bundles is mildly tangential but still short and potentially useful for discovery.

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 four-parameter, fully documented calculator with an output schema, the description covers purpose, context, inputs, and output adequately. The return-value sentence is redundant with the output schema, but nothing essential is missing.

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 every parameter is already documented. The description's input list (mean, std dev, sample size, confidence 90/95/99%) merely mirrors the schema, including the enum values, adding no format, unit, or constraint detail beyond it.

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 ('Compute confidence interval for a sample mean'), which is clearly distinct from neighbors like calculate_statistics or calculate_sample_size. It doesn't explicitly name which sibling to use instead, so it stops short of a 5.

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?

Gives concrete usage contexts ('statistics, A/B test results, or polling'), which is clear positive guidance. It offers no exclusions or named alternatives despite a very dense calculator sibling set, so it does not reach the explicit when/when-not bar of a 5.

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