The number of customers who enter a bank is thought to be Poisson distributed with a mean equal to 10 per hour. What are the chances that no customers will arrive in a 15-minute period?
A) Approximately zero
B) 0.0067
C) 0.0821
D) 0.0250

Question

Quizplus · Accepted Answer

The Poisson distribution formula for the probability of observing $k$ events in an interval is given by $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average number of events in an interval. For no customers ($k=0$) in a 15-minute period (which is a quarter of an hour), and with a mean ($\lambda$) of 10 customers per hour, the mean for 15 minutes is $10/4 = 2.5$. Substituting these values into the formula gives $P(0; 2.5) = \frac{e^{-2.5} 2.5^0}{0!} = e^{-2.5} \approx 0.0821$.

The Number of Customers Who Enter a Bank Is Thought