Answer:
0.6547 or 65.47%
Step-by-step explanation:
One minute equals 1/60 of an hour, the mean number of occurrences in that interval is:
[tex]\lambda =\frac{400}{60}=6.6667[/tex]
The poisson distribution is described by the following equation:
[tex]P(x) =\frac{\lambda^{x}*e^{-\lambda}}{x!}[/tex]
The probability that more than 5 vehicles will arrive is:
[tex]P(x>5)= 1-(P(0)+P(1)+P(2)+P(3)+P(4)+P(5))\\P(x>5) = 1-(\frac{6.667^{0}*e^{-6.667}}{1}+\frac{6.667^{1}*e^{-6.667}}{1}+\frac{6.667^{2}*e^{-6.667}}{2}+\frac{6.667^{3}*e^{-6.667}}{3*2}+\frac{6.667^{4}*e^{-6.667}}{4*3*2}+\frac{6.667^{5}*e^{-6.667}}{5*4*3*2})\\P(x>5)=1-(0.00127+0.00848+0.02827+ 0.06283+0.10473+0.13965)\\P(x>5)=0.6547[/tex]
The probability that more than five vehicles will arrive in a one-minute interval is 0.6547 or 65.47%.
