Answer:
[tex]P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}, X= 0,1,2,...[/tex]
[tex] P(X=8) = \frac{e^{-10.4} 10.4^8}{8!}= 0.1033[/tex]
And that would be the solution for this case.
Step-by-step explanation:
Previous concepts
The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:
[tex]P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}, X= 0,1,2,...[/tex]
Solution to the problem
Let X the random variable that represent the number of life insurance policies that the salesman person sells. We know that [tex]X \sim Poisson(\lambda=10.4)[/tex]
And we want to find this probability:
[tex] P(X =8)[/tex]
And we can use the probability mass function and we got:
[tex] P(X=8) = \frac{e^{-10.4} 10.4^8}{8!}= 0.1033[/tex]
And that would be the solution for this case.
