Question

During summer weekdays, boats arrive at the inlet drawbridge according to Poisson distribution at a rate of 3 per hour. In a 2-hour period, what is the probability that no boats arrive

Answer 1

Answer:

The probability that no boats arrive is $2.48\times 10^{-3}$.

Step-by-step explanation:

Poisson distribution:

Poisson distribution is a statistical distribution that helps to find out the probability of a certain is likely occur a specified period of time.

$P(X=x)=\frac{e^{-\lambda t}(\lambda t)^x}{x!}$

$\lambda$ = rate.

Given that, Poisson distribution at a rate of 3 per hour.

$\lambda$ = 3

t=2

x=0

The probability that no boats arrive is

$P(X=0)=\frac{e^{-2\times 3}(2\times 3)^0}{0!}$

                $=2.48\times 10^{-3}$