Answer: Our required probability is 0.0431.
Step-by-step explanation:
Since we have given that
X be the poisson distribution.
Mean rate = [tex]\dfrac{5}{10}=\dfrac{1}{2}=\lambda[/tex]
Number of toll = 8
We need to find the probability that he toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll.
So, mean will becomes,
[tex]\dfrac{1}{2}\times 26.30=13.15\ minutes[/tex]
Using the poisson distribution , we get that
[tex]P(X)=\dfrac{\lambda^x e^{-\lambda}}{x!}\\P(X\leq 8)=\dfrac{13.15^8 e^{-13.15}}{8!}\\\\P(X\leq 8)=0.0431[/tex]
Hence, our required probability is 0.0431.
