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We are studying deer population along an interstate highway. On average, there are 120 deer living...

We are studying deer population along an interstate highway. On average, there are 120 deer living within a three mile section on the highway. Assume the deer population follows the Poisson properties. Define the random variable x to be the number of deer we find within a certain length of highway. For all of the probability questions, show your work in Excel as demonstrated in class.

We are looking in a one mile section:

What is the expected number of deer in this section?

What is the probability we will find exactly 45 deer?

What is the probability we will find less than 45 deer?

What is the probability we will find more than 30 deer?

What is the probability we will find at least 30 deer?

Math   Statistics-And-Probability   
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Answer #1

(for work in excel formulas are put in bold so that you can copy and paste then in any cell)

1)expected number of deer in this section =120/3 =40

2)probability we will find exactly 45 deer =P(X=45)=poisson(45,40,false) =0.0440

3) probability we will find less than 45 deer=P(X<45)=poisson(44,40,true) =0.7657

4)  probability we will find more than 30 deer=P(X>30)=1-P(X<=30)=1-poisson(30,40,true)=0.9383

5)

probability we will find at least 30 deer =P(X>=30)=1-P(X<=29)=1-poisson(29,40,true)=0.9568

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