Exponential Distribution describes the times in between events a process in which events occur continuously and independently at a constant average rate.

If the number of occurrences of some event follows a Poisson distribution, the time between successive occurrences will follow an Exponential Distribution.

## Characteristics of an Exponential Distribution.

## When is the exponential distribution used?

- Describes the times in between events a process in which events occur continuously and independently at a constant average rate.
- To describe the time between successive occurrences when all occurrences follow an Exponential Distribution.
- To predict the length of time that properly maintained equipment will operate.
- To approximate the time between outcomes. (See Poisson)
- When a probability of an outcome is consistent throughout the time period.

http://www.public.iastate.edu/~riczw/stat330s11/lecture/lec13.pdf

## Six Sigma Black Belt Certification Exponential Distribution Questions:

**Question:** If a process follows an exponential distribution with a mean of 25, what is the standard deviation for the process? (Taken from ASQ sample Black Belt exam.)

(A) 0.4

(B) 5.0

(C) 12.5

(D) 25.0

**Answer:** 25.0. In an exponential distribution, the mean and standard deviations are equal.