Final answer:
In a service process, an inverse relationship exists between average processing time and coefficient of variation. With a constant standard deviation, as the average processing time decreases, the coefficient of variation increases, indicating the variability in the process relative to the mean is larger.
Step-by-step explanation:
The question is asking about the relationship between average processing time and the coefficient of variation in given service processes. The coefficient of variation is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean. Since the standard deviation is constant at two minutes, as the average processing time decreases, the ratio of the standard deviation to the mean increases, indicating a higher coefficient of variation.
For example, if the mean waiting time at the checkout is five minutes with a standard deviation of two minutes, the coefficient of variation is 0.4 (2/5). However, if the average wait time were to decrease to, say, three minutes with the same standard deviation, the new coefficient of variation would be approximately 0.67 (2/3), which is higher. Therefore, the relationship between the average processing time and the coefficient of variation is inverse; as the average processing time decreases, with a constant standard deviation, the coefficient of variation increases.