Final answer:
The statement regarding earthquakes in Papua New Guinea is used in a hypothetical context dealing with exponential distributions and does not provide enough information to be verified as true or false without further data.
Step-by-step explanation:
The statement that during the years 1998–2012, a total of 29 earthquakes of magnitude greater than 6.5 occurred in Papua New Guinea is marked as fact in the provided context.
Since this statement has been given in a hypothetical context for the purpose of teaching about exponential distributions, the truth of this statement in the real world is not verified, making the direct answer to the true/false question uncertain without further data.
Regarding the probabilities requested, the exponential nature of the time between earthquakes assumes a constant hazard rate over time. Thus, if enough data and the rate parameter were available, we could calculate the probability of an earthquake occurring within a given time frame.
However, it's very important to note that while the exponential distribution can be used for educational purposes, real-world earthquake prediction is highly complex and cannot be determined solely by such simple probabilistic models.