7 A statistics professor receives an average of five email m

7. 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. 0.0014 B. 0.0842 C. 0.4200 D. 0.0067

Solution

Given X~Poisson(mean=5)

P(X=x)=(5^x)*exp(-5)/x!

So the probability is

P(X=2) = (5^2)*exp(-5)/2= 0.08422434

Answer: B