Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two 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 two hours, and we want to find P(X = 6) for a five-hour period.First, we need to convert the rate from patients every two hours to patients per hour:λ = 3 patients / 2 hours = 1.5 patients / hourNow we can plug in the values into the Poisson distribution formula:P(X = 6) = (e^-1.5 * 1.5^6) / 6!= (0.2231 * 11.3906) / 720= 0.246Therefore, the probability of 6 patients arriving in a five-hour period is 0.246, or approximately 24.6%.

Historical Data Show That the Average Number of Patient Arrivals