Final answer:
Based on the information, it takes two minutes on average between two successive arrivals, and six minutes on average for three customers to arrive. To determine probabilities related to customer arrivals, one would need to consider an appropriate probability distribution, such as the exponential distribution, considering the properties of the customer arrivals.
Step-by-step explanation:
System Delivery Time and Customer Arrivals
The question appears to pertain to understanding customer arrival times and system delivery times which is typically covered in mathematics, specifically probability and statistics. Considering the information provided, we can answer the questions using the principles of these mathematical fields.
a. On average, how many minutes elapse between two successive arrivals?
Using the provided information, we can determine that since there is an average of one customer every two minutes, the time that elapses between two successive arrivals is two minutes.
b. When the store first opens, how long on average does it take for three customers to arrive?
Based on the average arrival rate of one customer every two minutes, it will take six minutes on average for three customers to arrive since the arrival of each customer is independent of the others.
d. After a customer arrives, find the probability that it takes more than five minutes for the next customer to arrive.
This scenario is less straightforward and would typically involve using a probability distribution, potentially exponential, to find the likelihood that more than five minutes will pass before the next customer arrives. Given just the average arrival rate, additional information or assumptions about the distribution are needed to calculate this probability.
e. Seventy percent of the customers arrive within how many minutes of the previous customer?
To determine this, we would expect to use a distribution that can describe the time between arrivals, like the exponential distribution. With sufficient data, we could calculate the time within which seventy percent of customers arrive following the previous customer.
f. Is an exponential distribution reasonable for this situation?
The use of an exponential distribution may be reasonable if customer arrivals are random and independent, with the average time between arrivals being constant. However, to confirm if this is an appropriate model, additional data analysis is required.