On average, Nancy has noticed that 27 trucks pass by her apartment daily ( 24 hours)....

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.

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Expert Solution

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

]

orchestra answered 1 year ago

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