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 no messages?
A)0.0067
B)0
C)0.0335
D)Impossible to have no messages

Question

Quizplus · Accepted Answer

The probability of receiving no messages in a Poisson distribution is calculated using the formula $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (5 messages per day in this case), and $k$ is the number of occurrences (0 messages). Plugging in the values, we get $P(X=0) = \frac{e^{-5} * 5^0}{0!} = e^{-5} \approx 0.0067$.

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