# QuantOracle Normal Distribution Calculator

> QuantOracle Normal Distribution Calculator is a paid API for AI agents from api.quantoracle.dev, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-15).

Computes normal distribution statistics including PDF, CDF, z-score, quantile, survival function, and confidence intervals for given mean, standard deviation, and value inputs

## Facts

- Endpoint: POST https://api.quantoracle.dev/v1/stats/normal-distribution
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/api-quantoracle-dev-456131b8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_NZwjUhgC5uM9HzXasLe_O

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability api-quantoracle-dev-456131b8 -d '<json body>'
```

Example prompt: For a normal distribution with mean 100 and standard deviation 15, what is the CDF, PDF, z-score, survival probability, and 95% confidence interval for the value 115?

## When to prefer this

Use this endpoint when you need a comprehensive set of normal distribution statistics in a single call — especially when you need CDF, PDF, z-score, quantile, survival function, and confidence interval together rather than computing them separately. Ideal for quantitative finance workflows, risk modeling, or any statistical analysis involving normally distributed data.

## Known failure modes

- Missing required fields (mean, std, x) returns a 4xx validation error
- Invalid confidence_level outside (0,1) range may return an error or unexpected results
- Non-numeric inputs for statistical parameters cause request failure
- Negative standard deviation is mathematically invalid and likely returns an error

## How this service works

QuantOracle: stats/normal-distribution

## Output

Returns a JSON object containing: CDF (cumulative distribution function), PDF (probability density function), z-score, quantile at probability p, survival function value, and a confidence interval object with lower/upper bounds and z-critical value, plus the echo of input parameters and execution time in milliseconds.

## Example request

```json
{
 "p": 0.95,
 "x": 115,
 "std": 15,
 "mean": 100,
 "confidence_level": 0.95
}
```

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "p": {
   "anyOf": [
    {
     "type": "number"
    },
    {
     "type": "null"
    }
   ],
   "title": "P",
   "description": "Probability for inverse CDF (quantile)"
  },
  "x": {
   "anyOf": [
    {
     "type": "number"
    },
    {
     "type": "null"
    }
   ],
   "title": "X",
   "description": "Value to compute CDF/PDF for"
  },
  "std": {
   "type": "number",
   "title": "Std",
   "default": 1,
   "description": "Distribution standard deviation",
   "exclusiveMinimum": 0
  },
  "mean": {
   "type": "number",
   "title": "Mean",
   "default": 0,
   "description": "Distribution mean"
  },
  "confidence_level": {
   "anyOf": [
    {
     "type": "number"
    },
    {
     "type": "null"
    }
   ],
   "title": "Confidence Level",
   "description": "Confidence level for interval (e.g. 0.95)"
  }
 }
}
```

## More

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