{"uid":"cap_v2vhzWdmsetXYLvpd9ZrJ","slug":"normal-distribution-calculator-pdf-cdf-quantile-02b0661a","name":"Normal Distribution Calculator (PDF, CDF, Quantile)","description":"Normal distribution with optional mean (default 0) and standard deviation sd (default 1). `function` selects the density (pdf), cumulative distribution (cdf) or quantile / inverse-CDF.","url":"https://distribution.openverbs.com/v1/normal","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType","body"],"properties":{"body":{"type":"object","required":["function","x"],"properties":{"x":{"type":"number","description":"Evaluation point: the variate for pdf/pmf/cdf, or the probability p ∈ (0,1) for quantile."},"sd":{"type":"number","description":"Standard deviation σ > 0. Default 1.","exclusiveMinimum":0},"mean":{"type":"number","description":"Mean μ. Default 0."},"function":{"enum":["pdf","cdf","quantile"],"type":"string"}},"additionalProperties":false},"type":{"type":"string","const":"http"},"method":{"enum":["POST"],"type":"string"},"bodyType":{"enum":["json","form-data","text"],"type":"string"}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.004","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.004/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.004","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_DUtyr4ch3BFbJ8jzqjNr5","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.004","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the probability density function (PDF), cumulative distribution function (CDF), or quantile (inverse CDF) for a normal (Gaussian) distribution given a mean, standard deviation, and evaluation point.","exampleAgentPrompt":"What is the cumulative probability (CDF) of a normal distribution with mean 0 and standard deviation 1 at x = 1.96?","exampleUseCases":[{"title":"Z-score significance test","prompt":"I need to know the two-tailed p-value for a z-score of 2.33 — can you give me the CDF of a standard normal distribution (mean 0, std 1) at x = 2.33?"},{"title":"IQ percentile lookup","prompt":"IQ scores are normally distributed with a mean of 100 and standard deviation of 15. What percentile (CDF) is someone with an IQ of 130?"},{"title":"Risk threshold quantile","prompt":"My model assumes returns are normally distributed with mean 0.05 and standard deviation 0.12. What return value corresponds to the bottom 5th percentile — i.e. the quantile at p = 0.05?"}],"resultDescription":"Returns a numeric result corresponding to the requested function: a probability density value (PDF), a cumulative probability between 0 and 1 (CDF), or a variate value (quantile/inverse CDF) for the given normal distribution parameters.","failureModes":["Standard deviation ≤ 0 returns a validation error (schema enforces exclusiveMinimum: 0)","Quantile called with x outside (0,1) returns an error since p must be a valid probability","Missing required fields (function or x) returns a 400-level error","Payment not included or insufficient balance returns a 402 Payment Required response"],"whenToPreferThis":"Choose this endpoint when you need fast, on-demand computation of normal distribution statistics (PDF, CDF, or quantile) without setting up a local statistics library. Ideal for AI agents performing probabilistic reasoning, hypothesis testing, or risk analysis that require a single clean API call rather than executing code. Particularly useful in sandboxed environments where running Python or R is not available.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T18:41:21.643Z","isFirstParty":false}