Assume that the number of customers who arrive at a water ice stand follows the Poisson distribution with an average rate of 6.4 per 30 minutes. What is the probability that exactly five customers will arrive during the next 30 minutes?
A)0.0943
B)0.3070
C)0.1487
D)0.0215

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a fixed interval of time in a Poisson distribution is given by the formula $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate of events per interval and $k$ is the number of events. Here, $\lambda = 6.4$ and $k = 5$. Plugging these values into the formula gives $P(5; 6.4) = \frac{e^{-6.4} \cdot 6.4^5}{5!}$, which calculates to approximately 0.1487.

Assume That the Number of Customers Who Arrive at a Water