Question

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.

Answer 1

Answer:

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