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**

Coughlin et al. (A-6) estimated the percentage of women living
in border counties along the southern
United States with Mexico (designated counties in California,
Arizona, New Mexico, and Texas) who
have less than a high school education to be 18.7. Assume the
corresponding probability is .19.
Suppose we select three women at random. Find the probability
that the number with less than a high-
school education is:
(a) Exactly zero (b) Exactly one
(c) More than one (d) Two or...

The occurrence of rust attacks along a gas pipeline can be
modeled as a Poisson process with intensity λ per kilometer. This
means that the number of rust attacks per kilometer along the
pipeline can be assumed to be Poisson distributed with expectation
value λ.
In the first instance, suppose that it is known that λ = 5.
a)
What is the probability of just two rust attacks in half a
kilometer?
What is the probability of more than two...

We might be interested in studying the proportion of children
living near a lead smelter who have colic. The prevalence of colic
in the general public is estimated to be as low as 7%. According to
collected data, there were 124 children and 23 of them had
colic.?
(a) Find the estimate the proportion of colicky infants. Give
answer up to two decimal places.
b. What will be the right hypotheses? The proportion of colic
among children living near lead...

The emergency telephone (911) center in a large city receives an
average of 120 calls per hour during a typical day. On average,
each call requires about 121 seconds for a dispatcher to receive
the emergency call, determine the nature and location of the
problem, and send the required individuals (police, firefighters,
or ambulance) to the scene. The center is currently staffed by 4
dispatchers a shift but must have an adequate number of dispatchers
on duty and it has...

Where are the deer? Random samples of square-kilometer plots
were taken in different ecological locations of a national park.
The deer counts per square kilometer were recorded and are shown in
the following table.
Mountain Brush
Sagebrush Grassland
Pinon Juniper
29
24
10
27
59
3
25
16
2
27
24
6
Shall we reject or accept the claim that there is no difference
in the mean number of deer per square kilometer in these different
ecological locations? Use a...

Where are the deer? Random samples of square-kilometer plots
were taken in different ecological locations of a national park.
The deer counts per square kilometer were recorded and are shown in
the following table.
Mountain Brush
Sagebrush Grassland
Pinon Juniper
34
15
1
31
58
7
24
15
10
25
26
13
Shall we reject or accept the claim that there is no difference
in the mean number of deer per square kilometer in these different
ecological locations? Use a...

The following problem is based on information from
Archaeological Surveys of Chaco Canyon, New
Mexico, by A. Hayes, D. Brugge, and W. Judge, University of
New Mexico Press. A transect is an archaeological study
area that is 1/5 mile wide and 1 mile long. A site in a
transect is the location of a significant archaeological find. Let
x represent the number of sites per transect. In a section
of Chaco Canyon, a large number of transects showed that x...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 18 transects gave a
sample variance s2 = 47.9 for...

A transect is an archaeological study area that is 1/5
mile wide and 1 mile long. A site in a transect is the
location of a significant archaeological find. Let x
represent the number of sites per transect. In a section of Chaco
Canyon, a large number of transects showed that x has a
population variance σ2 = 42.3. In a different
section of Chaco Canyon, a random sample of 25 transects gave a
sample variance s2 = 47.3 for...

A transect is an archaeological study area that is 1/5 mile wide
and 1 mile long. A site in a transect is the location of a
significant archaeological find. Let x represent the number of
sites per transect. In a section of Chaco Canyon, a large number of
transects showed that x has a population variance σ2 = 42.3. In a
different section of Chaco Canyon, a random sample of 26 transects
gave a sample variance s2 = 50.1 for...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 1 minute ago

asked 2 minutes ago

asked 4 minutes ago

asked 8 minutes ago

asked 10 minutes ago

asked 14 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 17 minutes ago