# 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 Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.

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Here,

• 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.

### Installation:

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)

Parameter:

• 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

Syntax:

mean(data)

• For standard deviation

Syntax:

std(data)

### Approach

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

Example:

## Python3

 from scipy.stats import normimport numpy as np  data_start = -5data_end = 5data_points = 11data = 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)print(probability_pdf)

Output:

0.0804410163156249

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