POISSON.DIST

Calculates the probability of a specific number of events occurring within a given interval of time, based on the Poisson distribution.

Syntax:

POISSON.DIST(x, mean, cumulative)

x is required, and is the number of events you are interested in the probability of.

mean is required, and is the average rate of occurrence of the event within the given interval.

cumulative is required, and is a logical value:

TRUE: Returns the cumulative probability of x or fewer events occurring.

FALSE: Returns the probability of exactly x events occurring.

Example:

If x contains 3, mean contains 5, and cumulative contains FALSE:

POISSON.DIST(3, 5, FALSE)

returns 0.140373896

This example finds the probability of exactly 3 visitors in a minute, when a website receives an average of 5 visitors per minute.

x:

mean:

Cumulative:

Result:

0.140373896

Application:

Calls to a Customer Service Center

Imagine a customer service center that receives an average of 15 calls per hour. We can use the POISSON.DIST function to analyze the probability of receiving a certain number of calls in a given hour.

Scenario: We want to find the probability of the following events:

Exactly 12 calls being received in the next hour.
12 or fewer calls being received in the next hour.

Parameters for the POISSON.DIST function:

x: The number of events we are interested in. In this case, it is 12.
Mean: The average number of events per interval. Here, it is 15 calls per hour.
Cumulative: This will be set to FALSE for the first question (exactly 12 calls) and TRUE for the second question (12 or fewer calls).

Calculations using POISSON.DIST:

	Question	x (Number of events)	Mean (Average)	Cumulative	POISSON.DIST Formula	Result (Probability)
	A	B	C	D	E	F
1	Probability of Exactly 12 Calls	12	15	FALSE	POISSON.DIST(12, 15, FALSE)	0.082859
2	Probability of 12 or Fewer Calls	12	15	TRUE	POISSON.DIST(12, 15, TRUE)	0.267611

Interpretation of Results:

The probability of the customer service center receiving exactly 12 calls in the next hour is approximately 8.29%.
The probability of the customer service center receiving 12 or fewer calls in the next hour is approximately 26.76%.