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 6 trucks will pass her apartment in a 6-hour time period using the Poisson distribution, find the average number of trucks per 6 hours. Round your answer to three decimal places, if necessary.

Answer 1

Answer: Our required probability is 0.384.

Step-by-step explanation:

Since we have given that

In  24 hours,

λ = 20

In 6 hours,

$\lambda=\dfrac{20}{24}\times 6=\dfrac{20}{4}=5$

As we know that it is a Poisson distribution.

E[X] = λ  = 5

Probability that more than 6 trucks will pass her apartment is given by

$P(X>6)=\sum_{x=6}^{20}\dfrac{e^{-5}\times 5^x}{x!}=0.384$

Hence, our required probability is 0.384.