In mornings and afternoons, the Newport Hospital emergency room can accommodate maximum of 12 patients in one hour, and the admissions procedure is designed to accommodate a maximum of five patients in one hour. Past experience suggest that for this hospital, an average of 28% of emergency room patients are admitted to the hospital for further care. We analyze the probability distribution of admission by considering a binomial distribution with n=12 and p= 0.28. Find the probability that when 12patients show up in the emergency room in one hour, the admissions procedure is overloaded. That is,find the probability of at least 6patients requiring admission, assuming that 12patients show up in the emergency room in one hour.
Is the probabibility of an overloaded admissions procedure small enough so that it does not happen very often, or does it seem too high so that changes must be made to make it lower?