Answer:
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
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 time interval.
20 cars per 10 minutes
So for 5 minutes, [tex]\mu = 10[/tex]
What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
This is P(X = 5).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378[/tex]
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
