Answer:
The probability of that there will be 5 accidents at this intersection is 0.1075.
Step-by-step explanation:
The Poisson distribution is used to explain the probability distribution of the number of events in a fixed interval.
Let X = number of accidents at the intersection.
Given: X follows Poisson distribution with mean, [tex]\lambda=3.1[/tex]
The probability distribution function of X is:
[tex]P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} \\=\frac{e^{-3.1}(3.1)^{x}}{x!}[/tex]
For X = 5 the probability is:
[tex]P(X=5)=\frac{e^{-3.1}(3.1)^{5}}{5!}\\=0.1075[/tex]
Thus, the probability of that there will be 5 accidents at this intersection is 0.1075.
