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Normal Distribution in NumPy - GeeksforGeeks

Last Updated : 23 Apr, 2025

The Normal Distribution also known as the Gaussian Distribution is one of the most important distributions in statistics and data science. It is widely used to model real-world phenomena such as IQ scores, heart rates, test results and many other naturally occurring events.

In Python's NumPy library we can generate random numbers following a Normal Distribution using the numpy.random.normal() method. It has three key parameters:

1. loc : Specifies the center (mean) of the distribution, where the peak of the bell curve exists.
2. scale : Determines the spread (standard deviation) of the distribution controlling how flat or narrow the graph is.
3. size : Defines the shape of the returned array.

numpy.random.normal(loc=0.0, scale=1.0, size=None)

To generate a single random number from a default Normal Distribution (loc=0, scale=1):

import numpy as np

random_number = np.random.normal()
print(random_number)

Output:

0.013289272641035141

To generate multiple random numbers

random_numbers = np.random.normal(size=5)
print(random_numbers)

Output:

[ 1.44819595 0.90517495 -0.75923069 0.50357022 -0.34776612]

Visualizing the generated numbers helps in understanding their behavior. Below is an example of plotting a histogram of random numbers generated using numpy.random.normal.

import numpy as np
import matplotlib.pyplot as plt

data = np.random.normal(loc=0, scale=1, size=1000)

plt.hist(data, bins=30, edgecolor='black', density=True)
pdf = norm.pdf(x, loc=loc, scale=scale)  
plt.plot(x, pdf, color='red', label='Theoretical PDF')
plt.title("Normal Distribution")
plt.xlabel("Value")
plt.ylabel("Density")
plt.grid(True)
plt.show()

Output:

The histogram represents the frequency of the generated numbers and the curve shows the theoretical pattern for comparison. The curve of a Normal Distribution is also known as the Bell Curve because of the bell-shaped curve.

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