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.

Explanation:

Since we have given that

In 24 hours,

λ = 20

In 6 hours,

`\lambda=(20)/(24)* 6=(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)(e^(-5)* 5^x)/(x!)=0.384`

Hence, our required probability is 0.384.