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A uniform distribution is a probability distribution in which every value between an interval from *a *to *b *is equally likely to be chosen.

The probability that we will obtain a value between x_{1} and x_{2} on an interval from *a *to *b *can be found using the formula:

P(obtain value between x_{1} and x_{2}) = (x_{2} – x_{1}) / (b – a)

To calculate probabilities related to the uniform distribution in Python we can use the scipy.stats.uniform() function, which uses the following basic syntax:

**scipy.stats.uniform(x, loc, scale)**

where:

**x**: The value of the uniform distribution**loc**: The minimum possible value**loc + scale**: The maximum possible value

The following examples show how to use this function in practice.

**Example 1**

Suppose a bus shows up at a bus stop every 20 minutes. If you arrive at the bus stop, what is the probability that the bus will show up in 8 minutes or less?

We can use the following code in Python to calculate this probability:

from scipy.stats import uniform #calculate uniform probability uniform.cdf(x=8, loc=0, scale=20) - uniform.cdf(x=0, loc=0, scale=20) 0.4

The probability that the bus shows up in 8 minutes or less is **0.4**.

**Example 2**

The weight of a certain species of frog is uniformly distributed between 15 and 25 grams. If you randomly select a frog, what is the probability that the frog weighs between 17 and 19 grams?

We can use the following code in Python to calculate this probability:

from scipy.stats import uniform #calculate uniform probability uniform.cdf(x=19, loc=15, scale=10) - uniform.cdf(x=17, loc=15, scale=10) 0.2

The probability that the frog weighs between 17 and 19 grams is** 0.2**.

**Example 3**

The length of an NBA game is uniformly distributed between 120 and 170 minutes. What is the probability that a randomly selected NBA game lasts more than 150 minutes?

We can use the following code in Python to calculate this probability:

from scipy.stats import uniform #calculate uniform probability uniform.cdf(x=170, loc=120, scale=50) - uniform.cdf(x=150, loc=120, scale=50) 0.4

The probability that a randomly selected NBA game lasts more than 150 minutes is **0.4**.

**Bonus:** You can double check the solution to each example by using the Uniform Distribution Calculator.

**Additional Resources**

The following tutorials explain how to use other common distributions in Python:

How to Use the Binomial Distribution in Python

How to Use the Poisson Distribution in Python

How to Use the t Distribution in Python