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# How to Use the Uniform Distribution in Excel

AÂ uniform distributionÂ is a probability distribution in which every value between an interval fromÂ aÂ toÂ bÂ is equally likely to be chosen.

The probability that we will obtain a value between x1Â and x2Â on an interval fromÂ aÂ toÂ bÂ can be found using the formula:

P(obtain value between x1Â and x2)Â  =Â  (x2Â â€“ x1) / (b â€“ a)

The uniform distribution has the following properties:

• The mean of the distribution isÂ Î¼Â = (a + b) / 2
• The variance of the distribution isÂ Ïƒ2Â = (b â€“ a)2Â / 12
• The standard deviation of the distribution isÂ ÏƒÂ =Â âˆšÏƒ2

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:Â 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 isÂ 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 isÂ 0.2.

Example 3:Â 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 isÂ 0.4.