In: Statistics and Probability
On average, Nancy has noticed that 27 trucks pass by her apartment daily ( 24 hours). In order to find the probability that more than 1 truck will pass her apartment in a 2 -hour time period using the Poisson distribution, find the average number of trucks per 2 hours. Round your answer to three decimal places, if necessary.
Solution:
Given: On average, Nancy has noticed that 27 trucks pass by her apartment daily ( 24 hours).
X = Number of trucks pass by Nancy's apartment daily ( 24 hours) follows a Poisson distribution with parameter per 24 hours.
We have to find the average number of trucks per 2 hours, so that we can find the probability that more than 1 truck will pass her apartment in a 2 -hour time period using the Poisson distribution.
Thus for 24 hours , we have average number of trucks =
then for 2 hours, the average number of trucks =
Thus the average number of trucks per 2 hours =
[
Thus the probability that more than 1 truck will pass her apartment in a 2 -hour time period is:
where
Thus
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