On average, Nancy has noticed that 20 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 2 trucks will pass her apartment in a 3-hour time period using the Poisson distribution, find the average number of trucks per 3 hours. Round your answer to three decimal places, if necessary.

P (2) = 0.256

Step-by-step explanation:

We know that Nancy has noticed that 20 trucks pass by her apartment daily (24 hours). We conclude that for 1 hours, pass 20/24=5/6 trucks.

We calculate how many trucks pass for 3 hours:

3 · 5/6 = 15/6=2.5=λ

We use a Poisson distribution:

P (k) = / frac{λ^k · e^{-λ}}{k!}

For 2 trucks we have that is k=2. We know that is λ=2.5

We caclulate the probability

P (2) = / frac{2.5² · e^{-2.5}}{2!}

P (2) = 0.256