For each one of the following situations, state whether a Poisson model is a plausible model over the specified time frame.
1. The process of arrivals of passengers to the baggage claim section of an airport
2. The process of order arrivals at an online retailer between 3:00 and 3:15 pm
3. The process of order arrivals at a local pizza delivery shop over the course of a day
incorrect
1. No
2. Yes
3. No
1. The process of arrivals of passengers to the baggage claim section of an airport: A Poisson model is a plausible model for this situation. The number of passengers arriving at the baggage claim section of an airport is likely to follow a Poisson distribution because the arrivals are independent of each other and occur randomly over time.
2. The process of order arrivals at an online retailer between 3:00 and 3:15 pm: A Poisson model might not be a plausible model for this situation. The number of order arrivals at an online retailer during a specific time frame like 3:00 and 3:15 pm could be influenced by various factors such as marketing campaigns, promotions, or customer behavior during specific times of the day. These factors might violate the assumptions of a Poisson process, which assumes a constant rate of arrival over time.
3. The process of order arrivals at a local pizza delivery shop over the course of a day: A Poisson model is generally a plausible model for this situation. The number of order arrivals at a local pizza delivery shop during a day could be approximated by a Poisson distribution. The assumption is that the orders arrive independently and follow a constant rate of arrival throughout the day.
To determine whether a Poisson model is a plausible model for each situation, we need to consider the characteristics of a Poisson process. A Poisson process is a counting process where events occur independently and at a constant average rate over time or space.
1. The process of arrivals of passengers to the baggage claim section of an airport:
A Poisson model is often a plausible model for this situation. However, it is important to note that the average rate of passenger arrivals should be approximately constant over the specified time frame. If there are significant fluctuations in the rate of passenger arrivals during the specified time frame, a Poisson model may not be appropriate.
2. The process of order arrivals at an online retailer between 3:00 and 3:15 pm:
In this case, a Poisson model is unlikely to be a plausible model. The specified time frame suggests a short time span, and it's common for online order arrivals to exhibit time-dependent patterns such as higher order rates during certain hours (e.g., lunchtime or after-work hours). A Poisson model assumes a constant average rate, which may not be reflective of the fluctuating order arrival patterns within this specific time frame.
3. The process of order arrivals at a local pizza delivery shop over the course of a day:
A Poisson model is usually not a plausible model for this situation. The order arrivals at a pizza delivery shop over the course of a day often exhibit time-dependent patterns, such as higher order rates during dinner hours and lower rates during late-night hours. A Poisson model assumes a constant average rate, which may not accurately capture the varying order arrival patterns throughout the day.
In summary, a Poisson model is more likely to be a plausible model for the process of arrivals of passengers at an airport baggage claim section, less likely for order arrivals at an online retailer within a short time frame, and not likely for order arrivals at a local pizza delivery shop over the course of a day. It is important to closely consider the characteristics of the process and the specific time frame when determining the appropriateness of a Poisson model.