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 five messages?
A) 0.0067
B) 0.875
C) 0.175
D) 1.0

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a fixed interval for a Poisson distribution is given by $P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!}$, where $\lambda$ is the average rate (mean) of occurrence and $k$ is the number of occurrences. Here, $\lambda = 5$ and $k = 5$, so $P(5; 5) = \frac{5^5 e^{-5}}{5!}$. Calculating this gives a probability of approximately 0.175.

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