Final answer:
The question seeks to determine idle time based on statistics but does not provide enough context or data to answer definitively.
Step-by-step explanation:
The question appears to be related to statistics, an area within mathematics that deals with data analysis. Idle time typically refers to the time when resources are available but not in use. Given the context provided, it seems the question concerns how idle time could be calculated based on statistical data; however, idle time isn't directly addressed in the information given, which centers on average wait times and excess time used by customers or riders.
Addressing the provided information, if we know that the 95th percentile for the sample mean excess time used is about 26.0 minutes, we might infer that only 5% of the time will the average excess time be more than 26 minutes.
The information about the probability that the mean excess time used is more than 20 minutes (0.7919) for a sample of 80 customers, helps us understand that it's quite likely for the mean time to exceed 20 minutes. Lastly, the comparison of a potential wait time of fewer than 30 minutes for 100 riders, given the data, would indeed be unexpected but is not impossible.
Unfortunately, without additional specific data relating to idle time calculation, we cannot provide a numerical answer to how much idle time will be present if 31 seconds are used.