Final answer:
On average, acute care hospital stays are shorter than 21 days, typically around 4-5 days. For the case of 80 women with maternity stays averaging more than five days, collectively they would exceed a year's stay in the hospital. Urgent care patient arrivals modeled with exponential distribution require probability computations for the given scenarios.
Step-by-step explanation:
The statement that the average length of stay for an acute care hospital is 21 days or less is generally false. Acute care hospital stays are often much shorter, particularly in the United States, where the average length of stay in acute care hospitals has been decreasing and is typically around 4-5 days, as reported by most recent data.
Considering the provided data that the average length of a maternity stay in a U.S. hospital is 2.4 days with a standard deviation of 0.9 days, for an individual to stay more than five days, it would be beyond the mean plus two standard deviations, which would be quite rare, given that such an occurrence would fall outside of the typical range seen for 95% of similar cases.
For the 80 women with an average stay of more than five days, collectively, if we calculate 80 (women) x 5 (days), we find they spent 400 days in the hospital, which is indeed more than a year. However, since it is mentioned that the average stay is more than five days, the total duration could be significantly higher.
As for the scenario involving urgent care facility patient arrivals being exponentially distributed with an average arrival rate of one every seven minutes, this requires the computation of probabilities related to the exponential distribution function for various time frames given in the question. Exponential distribution is often used in these circumstances to model the time between events in a Poisson process.