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) Zero
C) 0.0335
D) Impossible to have no messages

Question

Quizplus · Accepted Answer

The probability of receiving no messages (k=0) in a Poisson distribution with an average rate (λ) of 5 messages per day is calculated using the formula P(X=k) = (e^(-λ) * λ^k) / k!. Substituting the values, we get P(X=0) = (e^(-5) * 5^0) / 0! = e^(-5) ≈ 0.0067.

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