Answer :
Final answer:
The student's question requires knowledge of statistics and probability theory, specifically the Poisson and exponential distributions used to model the number and timing of events, such as phone calls, within a certain time frame.
Explanation:
The question falls under the category of Mathematics, specifically focusing on statistics and probability theory. As such, it requires an understanding of the Poisson distribution and exponential distribution, which are used to model the number of times an event occurs in a fixed interval of time or space and the time between events in a Poisson process, respectively.
For example, to determine the probability of receiving more than a certain number of calls within a specific time frame, one would generally use the Poisson distribution, characterized by the average rate of events (calls) per time interval. To find the probability that the interval between calls exceeds a given time (like three minutes), the exponential distribution is employed since it describes the time between consecutive Poisson events.
Therefore, to answer questions that involve finding the probability related to the number of calls or the timing between calls using the average rates provided, appropriate statistical formulas for the Poisson and exponential distributions should be used.
