Question

Assume that your statistics professor receives an average of five e-mail messages per day from students. If the number of messages approximates a Poisson distribution, what is the probability that on a randomly selected day your professor will have five messages?

Answer 1

Answer:  Our required probability is 0.175.

Step-by-step explanation:

Since we have given that

Average of 5 e-mails messages per day.

so, $\lambda=5$

We need to find the probability that on a randomly selected day your professor will have 5 messages.

Let X be the number of messages in poisson distribution.

So, P(X=5) is given by

$\dfrac{\lambda^xe^{-\lambda}}{x!}\\\\=\dfrac{5^5e^{-5}}{5!}\\\\=0.175$

Hence, our required probability is 0.175.