Answer :
Final Answer:
The Poisson distribution models the number of events occurring in a fixed interval of time or space, given a known average rate. In this case, with a mean of 11 people per hour, the parameter for the Poisson distribution is 11, indicating that on average, 11 people arrive at the emergency room per hour. The correct option is: a
Explanation:
The Poisson distribution is a probability distribution that describes the number of events occurring within a fixed interval of time or space, given a known average rate of occurrence and assuming events happen independently of each other. It's commonly used in various fields, including healthcare, to model scenarios where events happen randomly but at a predictable average rate.
In the context of an emergency room (ER) scenario, the Poisson distribution can effectively model the number of patients arriving per hour seeking medical attention.
In this case, with a mean of 11 people per hour, the Poisson distribution's parameter, often denoted by λ (lambda), is 11. This parameter represents the average rate at which events occur within the specified time or space interval. It indicates that, on average, 11 people arrive at the ER seeking medical attention every hour.
One fundamental property of the Poisson distribution is that it can model rare events occurring in a fixed interval, provided the average rate is constant and events are independent. For the ER example, although the arrival of patients might seem random, over a sufficiently long period, the average rate of arrivals tends to stabilize around 11 people per hour.
Understanding the Poisson distribution allows healthcare professionals and administrators to make informed decisions about resource allocation, staffing levels, and capacity planning.
By knowing the distribution of patient arrivals, hospitals can better anticipate and manage workload fluctuations, ensuring timely and effective care delivery while optimizing resource utilization.
Thus, the Poisson distribution serves as a valuable tool in healthcare operations management, aiding in the efficient functioning of emergency services.
