A statistic professor finds she averages 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
E) None of the choices are correct

Question

Quizplus · Accepted Answer

The probability of observing k events in a Poisson distribution is given by P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (5 messages), k is the number of events (2 messages), and e is approximately 2.71828. Plugging in the values, P(X=2) = (5^2 * e^(-5)) / 2! = 0.084.

A Statistic Professor Finds She Averages Five E-Mail Messages Per