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

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 rate (5 messages), k is the number of messages (5), and e is approximately 2.71828. Plugging in the values, P(X=5) = (5^5 * e^(-5)) / 5! = 0.175.

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