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#154easyStatistics

Z-Score Percentile

Part of:Statistics & Distributions → Normal Distribution & LLN

Problem

Given a normal distribution with mean mu and standard deviation sigma, compute the probability P(X≤x)P(X \le x).

This is equivalent to evaluating the cumulative distribution function (CDF) of the normal distribution at the point x.

Input Format

Three space-separated floating-point numbers: mu, sigma, and x.

Output Format

A single floating-point number to 6 decimal places representing P(X≤x)P(X \le x).

Examples

Example 1
Input(Three space-separated floating-point numbers: mu, sigma, and x.)
0 1 0
Output
0.500000

For standard normal, P(X <= 0) = 0.5 by symmetry.

Example 2
Input(Three space-separated floating-point numbers: mu, sigma, and x.)
100 15 130
Output
0.977250

z = (130-100)/15 = 2.0, P(X <= 130) = Phi(2.0) = 0.977250.

Constraints

  • •-1000 <= mu <= 1000
  • •0.001 <= sigma <= 1000
  • •-10000 <= x <= 10000

Execution limits: 2s · 256MB

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