Final answer:
The exponential distribution is used to calculate that 70 percent of customers arrive within 2.41 minutes of the previous customer, based on the expected average of one customer every two minutes.
Step-by-step explanation:
The question posed by the student is related to understanding customer arrival times and whether an exponential distribution is a suitable model for the scenario. If we expect 30 customers to arrive per hour (which is 60 minutes), this means, on average, we expect one customer every two minutes. The calculation to determine the time within which 70 percent of customers would arrive after a previous customer uses these figures and the properties of the exponential distribution.
In the context of the Square Root of N Rule, it is important to note that it is a different concept, often used in inventory management, which implies that, as the number of stocking locations increases, the overall inventory level does not need to double because you achieve efficiency through aggregation of demand variation. However, this rule is not directly applicable to the question about customer arrival times.
The use of the exponential distribution to model the time between customer arrivals is reasonable when the events (customer arrivals) are independent and occur at a constant average rate, which seems to be the case given the information.
Therefore, once we apply the exponential distribution model, we find that 70 percent of the customers arrive within 2.41 minutes of the previous customer, which corresponds to the 70th percentile of the distribution.
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