Probability distributions describe the likelihood of all possible outcomes of an event or experiment. The normal distribution is one of the most useful probability distributions because it models many natural phenomena very well. With NumPy, you can create random number samples from the normal distribution.
This distribution is also called the Gaussian distribution or simply the bell curve. The latter hints at the shape of the distribution when you plot it:
The normal distribution is symmetrical around its peak. Because of this symmetry, the mean of the distribution, often denoted by μ, is at that peak. The standard deviation, σ, describes how spread out the distribution is.
If some samples are normally distributed, then it’s probable that a random sample has a value close to the mean. In fact, about 68 percent of all samples are within one standard deviation of the mean.
You can interpret the area under the curve in the plot as a measure of probability. The darkly colored area, which represents all samples less than one standard deviation from the mean, is 68 percent of the full area under the curve.
In this tutorial, you’ll learn how you can use Python’s NumPy library to work with the normal distribution, and in particular how to create random numbers that are normally distributed. Along the way, you’ll get to know NumPy’s random number generator (RNG) and how to ensure that you can work with randomness in a reproducible manner.
You’ll also see how to visualize probability distributions with Matplotlib and histograms, as well as the effect of manipulating the mean and standard deviation. The central limit theorem explains the importance of the normal distribution. It describes how the average for any repeated experiment or measurement approximates the normal distribution.
As you’ll learn, you can do some powerful statistical analysis with the right Python code. To get the code from this tutorial, click the link below:
Free Bonus: Click here to download the free sample code that you’ll use to generate random numbers from a normal distribution in NumPy.
To follow along, you’ll need to install a few packages. First, create and activate a virtual environment. Then run the following pip command:
$ python -m pip install numpy matplotlib scipy
In addition to grabbing NumPy, you’ve installed Matplotlib and SciPy, so you’re ready to roll.
How to Use NumPy to Generate Normally Distributed Random Numbers
NumPy includes a full subpackage, numpy.random, dedicated to working with random numbers. For historical reasons, this package includes many functions. However, you should usually start by instantiating a default random number generator (RNG):
>>> import numpy as np
>>> rng = np