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 two customers will arrive during the next 15 minutes?
A)0.4236
B)0.2087
C)0.0778
D)0.1510

Question

Quizplus · Accepted Answer

The average rate of customers arriving at the stand is 6.4 per 30 minutes, so for 15 minutes, the average rate would be half of that, or 3.2 customers. 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 average rate, and $k$ is the number of events. Plugging in $\lambda = 3.2$ and $k = 2$, we get $P(2; 3.2) = \frac{e^{-3.2} * 3.2^2}{2!} = 0.2087$.

Assume That the Number of Customers Who Arrive at a Water