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)0.420
D)0.084

Question

Quizplus · Accepted Answer

The probability of receiving exactly k messages in a Poisson distribution is given by the formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average number of messages (5 in this case) and k is the number of messages we want the probability for (2 in this case). Plugging in the values, we get P(X=2) = (5^2 * e^(-5)) / 2! = 0.084.

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