# How to Use the Triangular Distribution in Excel (With Examples)

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 < x) = (x-a)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.