Final answer:
The objective of the customer arrival process is to maximize the conversion of arrivals to orders, with an average arrival rate of one customer every two minutes. Calculations based on this rate can determine expected wait times, but probabilities of customer arrival intervals require additional information on the distribution of those arrivals.
Step-by-step explanation:
The objective of the customer arrival process in a business context is to maximize the conversion of customer arrivals into customer orders. In operations involving customer queues, such as a restaurant or a retail store, this process is crucial for ensuring a smooth flow. Let's explore a few scenarios:
a. On average, how many minutes elapse between two successive arrivals?
Solution: Using given data, since there are 30 customers expected per hour, we calculate that on average, one customer arrives every two minutes.
b. When the store first opens, how long on average does it take for three customers to arrive?
Solution: Since one customer arrives every two minutes on average, it will take six minutes on average for three customers to arrive.
c. After a customer arrives, find the probability that it takes less than one minute for the next customer to arrive.
The given model assumes that arrivals are evenly spaced, which may not hold true in a real-world scenario and isn't given explicitly here, hence, cannot be accurately calculated without further information.
d. After a customer arrives, find the probability that it takes more than five minutes for the next customer to arrive.
Again, since the frequency of arrivals is one customer every two minutes on average, if customers arrive independently and at a constant rate, the probability of such an event is possible but cannot be concluded accurately without a specific distribution model (e.g., Poisson distribution).