Suppose the number of babies born during an 8-hour shift at a hospitalʹs maternity wing follows a Poissondistribution with a mean of 5 an hour. Find the probability that three babies are born during a particular1-hour period in this maternity wing.
A) 0.140374
B) 0.021780
C) 0.017547
D) 0.002053

Question

Quizplus · Accepted Answer

The probability of exactly k events in a Poisson distribution is given by $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of events per interval, and $k$ is the number of events. Here, $\lambda = 5$ (mean number of babies born per hour) and $k = 3$ (the number of babies we're interested in). Plugging these values into the formula gives $P(3; 5) = \frac{e^{-5} 5^3}{3!} = 0.140374$.

Suppose the Number of Babies Born During an 8-Hour Shift