# 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?

From the problem, we have the following given
u = 5
x = 0

We use the Poisson distribution probability formula:
P = (e^-μ) (μ^x) / x!
Substituting
P = (e^-5) (5^0) / 0!
P = 0.0067

The probability is 0.0067 or 0.67%

The probability that on a randomly selected day she will have no messages

Further Explanation:

The random variable X follows Poisson distribution.

Here, represents the Poisson parameter.

The mean of the Poisson parameter is

The variance of the Poisson parameter is

The formula for the probability of Poisson distribution can be expressed as follows,

Given:

The number of messages follows Poisson distribution.

The value of is

Explanation:

A statistics professor receives an average of five e-mail messages per day from students.

The mean of the message is 5.

The probability that on a randomly selected day she will have no messages can be obtained as follows,

The probability that on a randomly selected day she will have no messages

Subject: Statistics

Chapter: Poissondistribution

Keywords: statistics professor, receives, average, five e-mail, message, students, messages per day, Poisson distribution, probability, randomly selected, no message, parameter, probability formula, number of message.