Answer:
[tex]P(x = 0) = 0.061[/tex]
Step-by-step explanation:
Given
[tex]Average = 2.8[/tex]
Required
Determine the probability that no car will arrive.
Since it is a Poisson distribution, the required probability is:
[tex]P(x) = \frac{e^{-m}m^x}{x!}[/tex]
Where
[tex]m = average = 2.8[/tex]
In this case;
[tex]x = 0[/tex]
So:
[tex]P(x) = \frac{e^{-m}m^x}{x!}[/tex]
[tex]P(x = 0) = \frac{e^{-2.8}2.8^0}{0!}[/tex]
[tex]P(x = 0) = \frac{e^{-2.8}*1}{1}[/tex]
[tex]P(x = 0) = e^{-2.8}[/tex]
[tex]P(x = 0) = 0.06081006262[/tex]
[tex]P(x = 0) = 0.061[/tex] --- Approximated
