Final answer:
Customers arrive at the checkout every 6 minutes on average, meaning it takes 6 minutes for three customers to arrive. The exponential distribution can model the time between arrivals, assuming one customer arrives every 2 minutes, or 30 per hour. This model assumes a single customer arrives at intervals and a constant flow, which may not be fully accurate.
Step-by-step explanation:
When analyzing customer arrival and service rates at a fashion retailer with three cashiers, we can use the principles of probability and statistics to make inferences. Given that customers arrive every 6 minutes on average, we infer that when the store opens, it will take 6 minutes on average for three customers to arrive, assuming arrivals are evenly distributed.
The service rate will depend on how quickly each cashier can process a customer. If the service rate is slower than the arrival rate, queues will form, affecting the efficiency of the checkout process. Conversely, if the service rate is faster, cashiers will be idle at times. We can use the exponential distribution to model the time between successive arrivals, which indicates that there is a constant average rate of arrival. Using this distribution, the assumption is a continuous and memoryless process, meaning the probability of an event occurring in a fixed period of time is the same at any point.
For example, since we expect an average of one customer every two minutes (30 customers per hour), three customers would indeed take 6 minutes to arrive on average. This model, however, has limitations as it assumes a single customer arrives at a time and that the arrival flow is constant throughout the day, which may not reflect the actual shopping patterns accurately.