Normal distribution probability API

Compute normal-distribution probabilities for N(μ,σ): the CDF/PDF/survival at a point x, or an interval probability P(lower < X < upper) via the standard-normal CDF. Auditable: returns the z-score. Answers 'probability X is below 120','area under the normal curve between a and b','normal CDF for this value'.

Price$0.01per request

MethodPOST

Route/v1/calc/stat-normal-probability

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calcstatisticsnormalgaussianprobabilitycdfpdfdistribution

API URLhttps://x402.hexl.dev/v1/calc/stat-normal-probability

Integration docs

Example request

{
  "mean": 100,
  "sd": 15,
  "x": 120
}

Example response

{
  "mean": 100,
  "sd": 15,
  "x": 120,
  "zScore": 1.333333,
  "cdf": 0.90878872,
  "pdf": 0.010934,
  "survival": 0.09121128,
  "rating": "above median",
  "interpretation": "P(X ≤ 120) = 0.90879; z=1.3333."
}

Input schema

{
  "type": "object",
  "required": [
    "mean",
    "sd"
  ],
  "properties": {
    "mean": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "sd": {
      "type": "number",
      "description": "σ (>0)",
      "examples": [
        15
      ]
    },
    "x": {
      "type": "number",
      "description": "point for CDF/PDF",
      "examples": [
        120
      ]
    },
    "lower": {
      "type": "number",
      "description": "interval lower bound"
    },
    "upper": {
      "type": "number",
      "description": "interval upper bound"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}