Question

The number of cars arriving at a toll booth in five-minute intervals is poisson distributed with a mean of 3 cars arriving in five-minute time intervals. the probability of 5 cars arriving over a five-minute interval is _______.​

Answer 1

$P(k=5) = \frac{\lambda^k e^{-\lambda}}{k!} = \frac{3^5 e^{-3}}{5!} = 0.1008$

Answer 2

Answer:

The probability of 5 cars arriving over a five-minute interval is 0.1008 = 10.08%

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Mean of 3 cars arriving in five-minute time intervals.

This means that $\mu = 3$

The probability of 5 cars arriving over a five-minute interval is

This is P(X = 5).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008$

So

The probability of 5 cars arriving over a five-minute interval is 0.1008 = 10.08%