EXPON.DIST

Calculates the value of the exponential distribution.

Syntax:

EXPON.DIST(x, lambda, cumulative)

x is required, and is the value you want to use to evaluate the exponential distribution.

lambda is required, and is the rate parameter of the exponential distribution.

cumulative is required, and is a logical value:

TRUE: Returns the cumulative distribution function (CDF), which gives the probability that the random variable is less than or equal to x.

FALSE: Returns the probability density function (PDF), which gives the probability density at a specific value of x.

Example:

If x contains 3, lambda contains 1/5 and cumulative contains TRUE:

EXPON.DIST(3, 1/5, TRUE)

returns 0.451188364

This example calculates the probability that the next customer arrives within 3 minutes, when the average time between customer arrivals at a store is 5 minutes.

x:

Lambda:

Cumulative:

Result:

0.451188364

Application:

Time Between Customer Service Calls

Imagine you manage a customer service call center. You've analyzed historical data and found that, on average, your call center receives 10 calls per hour. You want to use the exponential distribution to answer some questions about the time between calls, assuming the rate of calls is constant.

The parameters for our EXPON.DIST function will be:

x: The time you are interested in (e.g., the time between two calls).
lambda (λ): The rate parameter. This is the average number of events per unit of time. In our case, the average is 10 calls per hour, so λ=10.
Cumulative: A logical value. TRUE returns the cumulative distribution function (CDF), which is the probability that the time between calls will be less than or equal to x. FALSE returns the probability density function (PDF), which is the probability of a specific, exact time x.

Let's use the EXPON.DIST function to find the probability of different time intervals between calls.

We will set up a table to calculate the cumulative probability. The formula we will use in a spreadsheet is EXPON.DIST(x, lambda, TRUE).

Probability of the Time Between Calls Being Less Than or Equal to a Certain Time (in hours)

	Time (x) in Hours	Formula	Probability (Cumulative)	Interpretation
	A	B	C	D
1	0.05	EXPON.DIST(0.05, 10, TRUE)	0.3935	There is a 39.35% chance that the time between two calls is 3 minutes or less.
2	0.1	EXPON.DIST(0.1, 10, TRUE)	0.6321	There is a 63.21% chance that the time between two calls is 6 minutes or less.
3	0.15	EXPON.DIST(0.15, 10, TRUE)	0.7769	There is a 77.69% chance that the time between two calls is 9 minutes or less.
4	0.2	EXPON.DIST(0.2, 10, TRUE)	0.8647	There is an 86.47% chance that the time between two calls is 12 minutes or less.
5	0.25	EXPON.DIST(0.25, 10, TRUE)	0.9179	There is a 91.79% chance that the time between two calls is 15 minutes or less.

How to Use the Table's Information:

This table provides valuable insights for the call center manager. For example, knowing that there's a nearly 63% chance of a new call arriving within 6 minutes of the last one helps in staffing decisions. It suggests that if a service representative is on a call, the next one is likely to be waiting shortly after the current one ends. This information can be used to optimize staffing levels, manage agent breaks, or predict the likelihood of calls stacking up in the queue.