How to Use the Uniform Distribution in Excel

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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 x₁ and x₂ on an interval from a to b can be found using the formula:

P(obtain value between x₁ and x₂)  =  (x₂ – x₁) / (b – a)

The uniform distribution has the following properties:

• The mean of the distribution is μ = (a + b) / 2
• The variance of the distribution is σ² = (b – a)² / 12
• The standard deviation of the distribution is σ = √σ²

The following examples show how to calculate probabilities for uniform distributions in Excel.

Note: You can double check the solution to each example below using the Uniform Distribution Calculator.

Examples: Uniform Distribution in Excel

Example 1: 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?

Solution:

• a: 0 minutes
• b: 20 minutes
• x₁: 0 minutes
• x₂: 8 minutes

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?

Solution:

• a: 15 grams
• b: 25 grams
• x₁: 17 grams
• x₂: 19 grams

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?

Solution:

• a: 120 minutes
• b: 170 minutes
• x₁: 150 minutes
• x₂: 170 minutes

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

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