A statistic professor finds she averages five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have two messages?
A) 0.0067
B) 0.0014
C) 0.420
D) 0.084
E) 0.5

Question

Quizplus · Accepted Answer

The probability of observing $k$ events in a fixed interval in a Poisson distribution is given by $P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!}$, where $\lambda$ is the average rate (mean) of events per interval, $k$ is the number of occurrences, and $e$ is the base of the natural logarithm (approximately equal to 2.71828). Given $\lambda = 5$ (average five email messages per day) and $k = 2$ (the probability of having two messages), the formula becomes $P(2; 5) = \frac{5^2 e^{-5}}{2!} = \frac{25 \cdot e^{-5}}{2} = 0.084$.

A Statistic Professor Finds She Averages Five E-Mail Messages Per