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.

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

`(\lambda^xe^(-\lambda))/(x!)\\\\=(5^5e^(-5))/(5!)\\\\=0.175`

Hence, our required probability is 0.175.