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Convert between a z-score and a percentile

zscore_percentile
Read-onlyIdempotent

Converts a z-score (standard deviations from the median) to a percentile and a percentile to a z-score on the normal curve, the relationship growth charts use. Pass exactly one of zScore or percentile. It converts the number and does not say what it means for a child.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
localeNoLanguage for the disclaimer and any clinician note. Pass the language you will answer the user in: these are clinical safety texts written by a paediatrician, and they should reach the reader as written rather than translated by the model.en
zScoreNoA z-score; returns the percentile.
percentileNoA percentile; returns the z-score.

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

A4.4/5.0
Behavior4/5

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

Annotations already establish read-only, idempotent, non-destructive, non-open-world behavior, so the description's job is lighter. It adds genuine semantic context: the conversion is mathematical only and carries no paediatric meaning, which prevents the agent from over-reading the result. It does not state what happens on invalid input or when both/neither parameter is supplied.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Three short sentences, front-loaded with the core transformation, then the invocation rule, then the scope boundary. Every sentence carries distinct information and nothing is repeated from the schema or annotations.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description does convey that the tool returns the counterpart value (percentile from z-score and vice versa), and the parameter descriptions confirm directionality. For a stateless two-way converter with read-only annotations, that is nearly sufficient; only the invalid-input/edge-case behavior is left unstated.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the baseline is 3 and the schema already documents zScore, percentile and the locale disclaimer text. The description adds real value beyond the schema by declaring the mutual-exclusivity constraint (exactly one of zScore or percentile), which the schema does not encode via oneOf. No error behavior for violating that rule is given.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific bidirectional transformation (z-score ↔ percentile) on the normal curve, and explicitly scopes it as a pure numeric conversion rather than a child-specific clinical measure. This distinguishes it from siblings like growth_percentile, bmi_percentile and growth_reference_range without opening any schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives an explicit invocation rule ('Pass exactly one of zScore or percentile') and a negative scope statement ('does not say what it means for a child'), which steers the agent away from using it for clinical interpretation. It never names the alternative tools to use when child-specific interpretation is wanted, so it falls short of a full when/when-not/alternative mapping.

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

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