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)

Uniform distribution example

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

Uniform distribution in Excel

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

Probability example with a uniform distribution in Excel

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

Uniform distribution probabilities in Excel

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

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