The manager of a movie theater has determined that the distribution of customers arriving at the concession stand is Poisson distributed with a standard deviation equal to 2 people per 10 minutes. What is the probability that more than 3 customers arrive during a 10-minute period?
A) 0.1804
B) 0.5665
C) 0.4335
D) 0.1954

Question

Quizplus · Accepted Answer

The standard deviation ($\sigma$) of a Poisson distribution is equal to the square root of its mean ($\lambda$). Given $\sigma = 2$, we find $\lambda = \sigma^2 = 4$. The probability of more than 3 customers arriving is 1 minus the probability of 3 or fewer, which can be calculated using the Poisson distribution formula or a table. Using a calculator or software for the cumulative Poisson probability, $P(X > 3) = 1 - P(X \leq 3)$ gives approximately 0.5665.

The Manager of a Movie Theater Has Determined That the Distribution