Final answer:
The questions involve calculating probabilities and averages for waiting times using uniform distribution principles. The probability of waiting less than 12.5 minutes for a bus that arrives every 15 minutes is 83.33%, and the average time between successive arrivals is two minutes.
Step-by-step explanation:
The questions presented relate to probability and uniform distribution, specifically in the context of waiting times for bus arrivals. To compute probabilities in a uniform distribution, the total range of possible outcomes and the range of the desired outcome are taken into account.
Probability of Waiting Fewer than 12.5 Minutes
For a bus that arrives every 15 minutes, the probability of waiting fewer than 12.5 minutes is simply the portion of the 15-minute interval that is less than 12.5 minutes. Thus, the probability is 12.5 divided by 15, which equals roughly 0.8333 or 83.33%.
Average Time Between Two Successive Arrivals
According to the given information, one customer arrives every two minutes on average. Therefore, the average time elapsed between two successive arrivals is two minutes.
Sample Average Wait Time for 100 Riders
The wait time is uniformly distributed from zero to 75 minutes. If 100 riders are sampled, we would expect the average wait time to be close to the midpoint of the distribution, which is (0+75)/2 = 37.5 minutes. Therefore, if the sample average was less than 30 minutes, it would be somewhat surprising as it is significantly lower than the expected average of 37.5 minutes.