The manager of the local grocery store has determined that, on the average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution.
-What is the probability that during a randomly selected half-hour period exactly 2 customers use the service desk?
A)0183
B)0733
C)1465
D)9084
E)7619

Question

Quizplus · Accepted Answer

The probability of exactly k events in a Poisson distribution is given by $P(k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (4 customers per half-hour in this case) and $k$ is the number of events (2 customers). Plugging in the values: $P(2) = \frac{e^{-4} 4^2}{2!} = \frac{e^{-4} \cdot 16}{2} = 8e^{-4}$. Calculating this gives approximately 0.1465, which corresponds to option C.

The Manager of the Local Grocery Store Has Determined That