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IBM

MCP Math Server

by IBM

normal_sample

Generate random samples from a normal distribution for statistical analysis and modeling. Specify sample size, mean, and standard deviation to create probability distributions.

Instructions

Generate random samples from the normal distribution (Domain: probability, Category: general)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
nYes
meanNo
stdNo
seedNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. The description mentions 'Generate random samples', implying a read-only operation that produces output, but it does not disclose any behavioral traits such as whether the tool is deterministic (e.g., with a seed parameter), what the output format is, or any performance considerations. This leaves significant gaps for a tool with 4 parameters and no output schema.

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

Conciseness4/5

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

The description is appropriately sized and front-loaded with the core purpose in a single sentence. It avoids unnecessary details and is efficient, though it could be slightly more informative without losing conciseness. Every sentence (only one) earns its place by stating the tool's function.

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

Completeness2/5

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

Given the complexity (a statistical sampling tool with 4 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It does not provide enough context for an AI agent to understand how to use the tool effectively, such as explaining parameter roles, output format, or usage scenarios. This is inadequate for a tool with multiple inputs and no structured output documentation.

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

Parameters1/5

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

The schema description coverage is 0%, meaning none of the 4 parameters (n, mean, std, seed) are documented in the schema. The description does not add any meaning beyond the schema—it does not explain what these parameters represent, their units, constraints, or default behaviors. For example, it does not clarify that 'n' is the sample size, 'mean' and 'std' define the distribution, or 'seed' controls randomness. This fails to compensate for the lack of schema documentation.

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

Purpose3/5

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

The description states the tool 'Generate random samples from the normal distribution', which specifies the verb ('Generate random samples') and resource ('normal distribution'), making the purpose clear. However, it does not distinguish this tool from sibling tools like 'uniform_sample' or 'binomial_sample', which also generate random samples from different distributions, leaving the differentiation vague.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain ('probability') and category ('general'), but this does not help an AI agent decide between this tool and other sampling tools like 'uniform_sample' or 'exponential_sample'. There are no explicit when/when-not instructions or named alternatives.

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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