Question

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.

What are the possible values of x?

We are looking in a three mile section:

What is the expected number of deer in this section?

What is the probability we will find exactly 150 deer?

What is the probability we will find less than or equal to 100 deer?

What is the probability we will find less than 100 deer?

What is the probability we will find more than 135 deer?

Answer 1

What are the possible values of x?

X follows poisson distribution with mean 120. Therefore X takes the following values.

X = { 0, 1, 2, ....}

What is the expected number of deer in this section?

The average of is = = 120

Therefore E(X) = = 120

What is the probability we will find exactly 150 deer?

Let's use excel:

P( X = 150) = "=POISSON(150,120,0)" = 0.001011

What is the probability we will find less than or equal to 100 deer?

P( X <= 100) = "=POISSON(100,120,1)" = 0.034668

What is the probability we will find less than 100 deer?

P( X < 100) = P(X <= 100 - 1) = P(X <= 99) = "=POISSON(99,120,1)" = 0.027864

What is the probability we will find more than 135 deer?

P( X > 135 ) = 1 - P( X <= 135) = "=1-POISSON(135,120,1)" = 0.080616