# How to Use the Uniform Distribution in Excel

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

The probability that we will obtain a value between x1 and x2 on an interval from to 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

### 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.