Answer:
0.000005 probability that exactly 9 cars arrive between 12:10 and 12:20.
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.
Mean of 3 cars per minute:
So, between 12:10 and 12:20, there is an interval of 10 minutes, which means that [tex]\mu = 3*10 = 30[/tex]
What is the probability that exactly 9 cars arrive between 12:10 and 12:20?
This is [tex]P(X = 9)[/tex]. So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 9) = \frac{e^{-30}*30^{9}}{(9)!} = 0.000005[/tex]
0.000005 probability that exactly 9 cars arrive between 12:10 and 12:20.
