Final answer:
The student's question involves calculating average interarrival times for customers and the probability of certain arrival-related events, assuming customers arrive at a constant rate, with additional questions about percentiles and distribution suitability.
Step-by-step explanation:
The student's question pertains to the average time between the arrival of customers and the probability of certain events related to customer arrivals and interaction times. If there are 30 customers expected to arrive per hour, this translates to an average arrival rate of one customer every two minutes. The average time for three customers to arrive would be two minutes times three, resulting in six minutes.
For part d, if you are given a probability distribution, you could use that information to calculate the probability that more than five minutes will elapse before the next customer arrives. In the provided examples, probabilities are calculated based on various durations (e.g., four to five minutes in Example 5.8). Without a specific distribution, it's not possible to calculate the exact probability, but an exponential distribution, often used for this type of analysis, implies that longer interarrival times become increasingly less likely.
Finally, part e asks for the 70th percentile, which indicates the time within which 70 percent of customers arrive following a previous customer. If the analysis suggests that 70 percent of customers arrive within 2.41 minutes, that time duration is the answer to part e.