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How to calculate probability in a normal distribution given mean and standard deviation in Python?
  • Last Updated : 25 Feb, 2021

A normal distribution is a type of continuous probability distribution for a real-valued random variable. It is based on mean and standard deviation. The probability distribution function or PDF computes the likelihood of a single point in the distribution. The general formula to calculate PDF for the normal distribution is

 f_X(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{\frac{-1}{2}\big( \frac{x-\mu}{\sigma} \big)^2}\\


  • µ is the mean
  • σ is the standard deviation of the distribution
  • x is the number

for which PDF is to be calculated.. We can calculate probability in a normal distribution using SciPy module.


pip install scipy

Function used:

We will use scipy.stats.norm.pdf() method to calculate the probability distribution for a number x.

Syntax: scipy.stats.norm.pdf(x, loc=None, scale=None)


  • x : array-like object, for which probability is to be calculated.
  • loc : optional (default=0), represents mean of the distribution.
  • scale : optional (default=1), represents standard deviation of the distribution.

Returns: A probability density function calculated at x as a ndarray object.

In scipy the functions used to calculate mean and standard deviation are mean() and std() respectively.

  • For mean



  • For standard deviation




  • Import module
  • Create necessary data
  • Supply the function with required values
  • Display value



from scipy.stats import norm
import numpy as np
data_start = -5
data_end = 5
data_points = 11
data = np.linspace(data_start, data_end, data_points)
mean = np.mean(data)
std = np.std(data)
probability_pdf = norm.pdf(3, loc=mean, scale=std)



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