Final answer:
We must greet customers within 10-30 seconds
Step-by-step explanation:
The question is related to customer service in a business setting, specifically about the timeliness of greeting customers as they arrive. Given the provided information, we can infer that there is an expectation related to the time frame in which a customer should be greeted.
In the provided solution, we can deduce that if customers are arriving on average every two minutes, the business may want to ensure that each customer is greeted promptly, potentially within seconds of arrival. However, the specific number of seconds is not provided in the solution.
Businesses may set their own standards, commonly aiming to greet customers within 10-30 seconds to ensure a positive customer experience. Therefore, when responding to this customer service policy question, one would need additional information or context provided by the business's guidelines to give an exact number of seconds within which to greet customers.
From the additional details given, we learn about the arrival rate of customers, which can help in planning customer service strategies. For example, knowing that 70 percent of customers arrive within 2.41 minutes of the previous customer could influence the standard greeting time.
In this scenario, using an exponential distribution to model customer arrival times seems reasonable, as indicated by the data showing the 90th percentile of wait time in line as 13.5 minutes and the 95th percentile for sample mean excess time as 26.0 minutes for a random sample of 80 customers.