If a process follows an exponential distribution with a mean of 25, what is the standard deviation for the process?

• A. 0.4
• B. 5.0
• C. 12.5
• D. 25.0

Answer: (D)

For an exponential distribution, the standard deviation is equal to the mean. This property arises from the mathematical characteristics of the exponential distribution, which is commonly used to model time until an event occurs, such as the time until failure of a system or time between arrivals in a queuing system.

Given that the mean of the distribution is 25, the standard deviation is also 25. This direct relationship means that if the average time until an event occurs is 25 units, the dispersion or variability around this average (the standard deviation) will also show that same width of spread, which is 25.

To summarize, in an exponential distribution, both the mean and standard deviation are quantitatively the same, leading to the conclusion that the standard deviation for a process with a mean of 25 is indeed 25.