Respuesta :
Answer:
6.07% probability that exactly 5 claims will be filed during the next week.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
An average of 9 claims are filed in its Denver branch.
So [tex]\mu = 9[/tex]
What is the probability that exactly 5 claims will be filed during the next week?
This is [tex]P(X = 5)[/tex].
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 5) = \frac{e^{-9}*(9)^{5}}{(5)!} = 0.0607[/tex]
6.07% probability that exactly 5 claims will be filed during the next week.
