The triangular distribution is a continuous probability distribution with a probability density function shaped like a triangle.
It is defined by three values:
- The minimum value a
- The maximum value b
- The peak value c
The name of the distribution comes from the fact that the probability density function is shaped like a triangle.
The triangular distribution has the following PDF and CDF:
PDF:
CDF:
The following examples show how to use the Triangular distribution to calculate probabilities in Excel.
Example 1: Restaurant Sales
Suppose a restaurant estimates that their total sales for the upcoming week will be a minimum of $10,000, a maximum of $30,000, and most likely $25,000.
What is the probability that the restaurant makes less than $20,000 total sales?
According to the CDF, we can use the following formula to find the probability that total sales will be less than $20,000:
- P(X 2 / ((b-a)(c-a))
Here’s how to calculate this probability in Excel:
The probability that the restaurant makes less than $20,000 total sales is .333.
Example 2: Number of Customers
Suppose a shop estimates that the number of customers that will enter in a given week will be a minimum of 500, a maximum of 2,000, and most likely 1,200.
What is the probability that more than 1,500 customers enter the shop in a given week?
According to the CDF, we can use the following formula to find the probability that the total number of customers will be greater than 1,500:
- P(X > x) = 1 – [1 – (b-x)2 / ((b-a)(b-c))]
Here’s how to calculate this probability in Excel:
The probability that more than 1,500 customers enter the shop is .208.
Additional Resources
The following tutorials explain how to work with other probability distributions in Excel:
How to Use the Binomial Distribution in Excel
How to Use the Poisson Distribution in Excel
How to Use the Uniform Distribution in Excel