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How to Use the Uniform Distribution in Excel?

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An example of a probability distribution where all possibilities are equally likely is called a uniform distribution. Since all four suits—heart, club, diamond, and spade—have an equal chance of appearing, a deck of cards has uniform distributions throughout. The chance of receiving either heads or tails in a coin toss is the same, hence a coin also has a uniform distribution. The easiest probability distribution to build in Excel is the uniform distribution. A uniform distribution is a probability distribution in which there is an equal chance of selecting any value between a and b. 

The following formula can be used to calculate the probability that a value between x1 and x2 will fall within the range from a to b:

P = (x2 – x1) / (b – a)

Where P is the calculated value between x1 and x2

Uniform Distribution

 

For calculating probability, we need:

  1. a: minimum value in the distribution
  2. b: maximum value in the distribution
  3. x1: the minimum value you’re interested in
  4. x2: the maximum value you’re interested in

Then just by using the formula mentioned above, you can easily calculate the chances or probability of anything.

The characteristics of the uniform distribution are as follows:

The distribution’s average is equal to (a + b) / 2 = μ
The distribution’s variance is σ2 = (b – a)2 / 12
The distribution’s standard deviation is σ = √σ2

How to calculate probability will be clear with the following Example

Example 1: A certain kind of bird has a weight range of 37.25 to 584.32 grams that are equally distributed throughout. What is the chance that a bird will weigh between 100.89 and 477.63 grams if a bird is randomly chosen?

Step 1: First you need to write all these given values in an excel sheet.

a (minimum value in distribution) = 37.25

b (maximum value in distribution) = 584.32

x1 (minimum value you’re interested in) = 100.89

x2 (maximum value you’re interested in) = 477.63

Entering a value in excel.

Entering a value in excel

Step 2: For calculating the probability you need to use the formula (x2-x1)/(b-a). Here we enter this enter =(B4-B3)/(B2-B1) because the value of x2 stores in cell B4, the value of x1 stores in cell B3, the value of b stores in cell B2, and the value of a is stored in the cell B1.

Entering the formula for calculating the probability.

Entering the formula for calculating the chance

Step 3: Press enter then we will get the probability value which is our answer.

Final output.

calculated value

Hence, the chance that a bird will weigh between 100.89 and 477.63 grams if a bird is randomly chosen is 0.68865.

Example 2: Every 10 minutes, a bus gets up to a bus stop. What is the chance that the bus will arrive in 5 minutes or less if you arrive at the bus stop?

Step 1: First you need to write all these given values in an excel sheet.

a (minimum value in distribution) = 0

b (maximum value in distribution) = 10

x1 (minimum value you’re interested in) = 0

x2 (maximum value you’re interested in) = 5

Entering a value in excel.

 

Step 2: For calculating the probability you need to use the formula (x2-x1)/(b-a). Here we enter =(B4-B3)/(B2-B1) because the value of x2 stores in cell B4, the value of x1 stores in cell B3, the value of b stores in cell B2, and the value of a is stored in cell B1.

Entering the formula for calculating the probability.

 

Step 3: Press enter then we will get the probability value which is our answer.

Final output.

 

Hence, the chance that the bus will arrive in 5 minutes or less if you arrive at the bus stop is 0.5


Last Updated : 01 Mar, 2024
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