A statistics professor receives an average of 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)0.4200
D)0.0842

Question

Quizplus · Accepted Answer

The probability of receiving exactly k messages in a Poisson distribution is given by $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (5 messages per day in this case) and $k$ is the number of occurrences (2 messages). Plugging in the values: $P(2; 5) = \frac{e^{-5} 5^2}{2!} = \frac{e^{-5} \cdot 25}{2} = 0.0842$.

A Statistics Professor Receives an Average of Five E-Mail Messages