Respuesta :
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%
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 [tex]\boxed{0.00674}.[/tex]
Further Explanation:
The random variable X follows Poisson distribution.
[tex]\boxed{X\~{\text{Poisson}}\left( \lambda \right)}[/tex]
Here, [tex]\lambda[/tex] represents the Poisson parameter.
The mean of the Poisson parameter is [tex]\lambda.[/tex]
The variance of the Poisson parameter is [tex]\lambda.[/tex]
The formula for the probability of Poisson distribution can be expressed as follows,
[tex]\boxed{P\left( x \right)=\frac{{{e^{- \lambda }}\times {\lambda ^x}}}{{x!}}}[/tex]
Given:
The number of messages follows Poisson distribution.
The value of [tex]\lambda[/tex] is [tex]\lambda = 5.[/tex]
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,
[tex]\begin{aligned}P\left( 0 \right) &= \frac{{{e^{ - 5}} \times {5^0}}}{{0!}}\\&= \frac{{0.00674 \times 1}}{1}\\&= 0.00674\\\end{aligned}[/tex]
The probability that on a randomly selected day she will have no messages [tex]\boxed{0.00674}.[/tex]
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of meanhttps://brainly.com/question/12986589
Answer details:
Grade: College
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.
