Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours.Assume that the patient arrivals are distributed according to Poisson distribution. Determine the probability of 6 patients arriving in a five-hour period.
A).136
B).109
C).246
D).001

Question

Quizplus · Accepted Answer

The probability of 6 patients arriving in a five-hour period can be calculated using the Poisson distribution formula:P(X = k) = (e^-λ * λ^k) / k!where:λ is the average number of arrivals per unit timek is the number of arrivalsIn this case, λ = 3 patients every 2 hours, and k = 6 patients. We need to convert λ to the number of arrivals per 5 hours:λ = 3 patients / 2 hours * 5 hours / 1 = 7.5 patients / 5 hoursNow we can calculate the probability:P(X = 6) = (e^-7.5 * 7.5^6) / 6! = 0.136Therefore, the probability of 6 patients arriving in a five-hour period is 0.136, or 13.6%.

Historical Data Shows That the Average Number of Patient Arrivals