Answer:
There is a 3.33% probability that exactly two such busses arrive within 3 minutes of each other.
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.
What is the probability that exactly two such busses arrive within 3 minutes of each other
The mean is one bus each 10 minutes. So for 3 minutes, the mean is 3/10 = 0.3 buses. So we use [tex]\mu = 0.3[/tex]
This probability is P(X = 2).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 2) = \frac{e^{-0.3}*(0.3)^{2}}{(2)!} = 0.0333[/tex]
There is a 3.33% probability that exactly two such busses arrive within 3 minutes of each other.
