Internet Field trip

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  1. Research: Research at least six (6) information sources on forecasting methods; take notes and record and interpret significant facts, meaningful graphics, accurate sounds and evaluated alternative points of view.
    1. Preparation: Produce as storyboard with thumbnails of at least ten (10) slides. Include the following elements:
    • Title of slide, text, background color, placement & size of graphic, fonts – color, size, type for text and headings
    • Hyperlinks (list URLs of any site linked from the slide), narration text, and audio files (if any)
    • Number on slides clear
    • Logical sequence to the presentation
    1. Content: Provide written content with the following elements:
    • introduction that presents the overall topic (clear sense of the project’s main idea) and draws the audience into the presentation with compelling questions or by relating to the audience’s interests or goals.
    • accurate, current
    • clear, concise, and shows logical progression of ideas and supporting information
    • motivating questions and advanced organizers
    • drawn mainly from primary sources
    1. Text Elements: Slides should have the following characteristics:
    • fonts are easy-to-read; point size that varies appropriately for headings and text
    • italics, bold, and indentations enhance readability
    • background and colors enhance the readability of text
    • appropriate in length for the target audience; to the point
    1. Layout: The layout should have the following characteristics:
    • visually pleasing
    • contributes to the overall message
    • appropriate use of headings, subheadings and white space
    1. Media: The graphics, sound, and/or animation should
    • assist in presenting an overall theme and enhance understanding of concept, ideas and relationships
    • have original images that are created using proper size and resolution; enhance the content
    • have a consistent visual theme.
    1. Citations: The sources of information should:
    • properly cited so that the audience can determine the credibility and authority of the information presented
    • be properly formatted according to APA style

MAT 540 Week 8 Homework

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MAT540

Week 8 Homework

Chapter 4

14.   Grafton Metalworks Company produces metal alloys from six different ores it mines.  The company has an order from a customer to produce an alloy that contains four metals according to the following specifications:  at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of metal D.  The proportion of the four metals in each of the six ores and the level of impurities in each ore are provided in the following table:

Ore

Metal (%)

Impurities (%)

Cost/Ton

A

B

C

D

1

19

15

12

14

40

27

2

43

10

25

7

15

25

3

17

0

0

53

30

32

4

20

12

0

18

50

22

5

0

24

10

31

35

20

6

12

18

16

25

29

24

 

When the metals are processed and refined, the impurities are removed. 

The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy.

a.        Formulate a linear programming model for this problem. 

b.      Solve the model by using the computer. 

 

19.   As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs and projects.  It is up to the congressman to decide how to distribute the money.  The congressman has decided to allocate the money to four ongoing programs because of their importance to his district – a job training program, a parks project, a sanitation project, and a mobile library.  However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election.  His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows.

 

Program

Votes/ Dollar

Job training

0.02

Parks

0.09

Sanitation

0.06

Mobile library

0.04

 

In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following guidelines:

·         None of the programs can receive more than 40% of the total allocation.

·         The amount allocated to parks cannot exceed the total allocated to both the sanitation  project and the mobile library

·         The amount allocated to job training must at least equal the amount spent on the sanitation project. 

Any money not spent in the district will be returned to the government; therefore, the congressman wants to spend it all.  The congressman wants to know the amount to allocate to each program to maximize his votes. 

a.       Formulate a linear programming model for this problem.

b.      Solve the model by using the computer.

 

20.   Anna Broderick is the dietician for the State University football team, and she is attempting to determine a nutritious lunch menu for the team.  She has set the following nutritional guidelines for each lunch serving:

·         Between 1,500 and 2,000 calories

·         At least 5 mg of iron

·         At least 20 but no more than 60 g of fat

·         At least 30 g of protein

·         At least 40 g of carbohydrates

·         No more than 30 mg of cholesterol

She selects the menu from seven basic food items, as follows, with the nutritional contributions per pound and the cost as given: 

 

Calories

(per lb.)

Iron

(mg/lb.)

Protein

(g/lb.)

Carbo-hydrates

(g/lb.)

Fat (g/lb.)

Chol-esterol

(mg/lb.)

Cost

 

$/lb.

Chicken

520

4.4

17

0

30

180

0.80

Fish

500

3.3

85

0

5

90

3.70

Ground beef

860

0.3

82

0

75

350

2.30

Dried beans

600

3.4

10

30

3

0

0.90

Lettuce

50

0.5

6

0

0

0

0.75

Potatoes

460

2.2

10

70

0

0

0.40

Milk (2%)

240

0.2

16

22

10

20

0.83

 

The dietician wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving.

a.       Formulate a linear programming model for this problem.

b.      Solve the model by using the computer

c.       If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution?

 

22.   The Cabin Creek Coal (CCC) Company operates three mines in Kentucky and West Virginia, and it supplies coal to four utility power plants along the East Coast.  The cost of shipping coal from each mine to each plant, the capacity at each of the three mines and the demand at each plant are shown in the following table:

 

 

Plant

 

Mine

1

2

3

4

Mine Capacity (tons)

1

 $ 7

$ 9

$10

$12

220

2

9

7

8

12

170

3

11

14

5

7

280

Demand (tons)

110

160

90

180

 

 

The cost of mining and processing coal is $62 per ton at mine 1,  $67 per ton at mine 2, and  $75 per ton at mine 3.  The percentage of ash and sulfur content per ton of coal at each mine is as follows:

 

Mine

% Ash

% Sulfur

1

9

6

2

5

4

3

4

3

 

 

Each plant has different cleaning equipment.  Plant 1 requires that the coal it receives have no more than 6% ash and 5% sulfur; plant 2 coal can have no more than 5% ash and sulfur combined; plant 3 can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than 6% ash and sulfur combined.    CCC wabts to determine the amount of coal to produce at each mine and ship to its customers that will minimize its total cost. 

 

a.       Formulate a linear programming model for this problem.

b.      Solve this model by using the computer.

 

 

36.   Joe Henderson runs a small metal parts shop. The shop contains three machines – a drill press, a lathe, and a grinder.   Joe has three operators, each certified to work on all three machines.  However, each operator performs better on some machines than on others.  The shop has contracted to do a big job that requires all three machines.  The times required by the various operators to perform the required operations on each machine are summarized as follows: 

 

Operator

Drill Press (min)

Lathe (min)

Grinder (min)

1

23

18

35

2

41

30

28

3

25

36

18

 

 

Joe Henderson wants to assign one operator to each machine so that the topal operating time for all three operators is minimized.

a.       Formulate a linear programming model for this problem. 

b.      Solve the model by using the computer

c.       Joe’s brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator.  Kelly can perform each of the three required machine operations in 20 minutes.  Should Joe hire his sister-in-law? 

 

43.   The Cash and Carry Building Supply Company has received the following order for boards in three lengths:

Length

Order (quantity)

7 ft.

700

9 ft.

1,200

10 ft.

300

 

The company has 25-foot standard-length boards in stock.  Therefore, the standard-length boards must be cut into the lengths necessary to meet order requirements.  Naturally, the company wishes to minimize the number of standard-length boards used. 

               

a.       Formulate a linear programming model for this problem. 

b.      Solve the model by using the computer

c.       When a board is cut in a specific pattern, the amount of board left over is referred to as “trim-loss.” Reformulate the linear programming model for this problem, assuming that the objective is to minimize trim loss rather than to minimize the total number of boards used, and solve the model.  How does this affect the solution? 

 

 

 

 

Multi Choice Problems

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Question 1 of 20
 0.0/ 5.0 Points
Halley’s comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley’s comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.
A. 12.13 astronomical units; 1128 million miles  
B. 91.54 astronomical units; 8513 million miles  
C. 5.69 astronomical units; 529 million miles  
D. 6.06 astronomical units; 564 million miles  

Question 2 of 20
 0.0/ 5.0 Points
Use the center, vertices, and asymptotes to graph the hyperbola.

(x – 1)2 – 9(y – 2)2= 9
A.  
B.  
C.  
D.  

Question 3 of 20
 0.0/ 5.0 Points
Find the standard form of the equation of the ellipse and give the location of its foci.
A. + = 1
foci at (- , 0) and ( , 0)		  
B. – = 1
foci at (- , 0) and ( , 0)		  
C. + = 1
foci at (- , 0) and ( , 0)		  
D. + = 1
foci at (-7, 0) and ( 7, 0)		  

Question 4 of 20
 0.0/ 5.0 Points
Rewrite the equation in a rotated x’y’-system without an x’y’ term. Express the equation involving x’ and y’ in the standard form of a conic section.

31x2 + 10xy + 21y2-144 = 0
A. x‘2 = -4 y’  
B. y‘2 = -4x’  
C. + = 1  
D. + = 1  

Question 5 of 20
 0.0/ 5.0 Points
Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5
A. + = 1  
B. + = 1  
C. + = 1  
D. + = 1  

Question 6 of 20
 0.0/ 5.0 Points
Find the vertices and locate the foci for the hyperbola whose equation is given.

49x2 – 100y2= 4900
A. vertices: ( -10, 0), ( 10, 0)
foci: (- , 0), ( , 0)		  
B. vertices: ( -10, 0), ( 10, 0)
foci: (- , 0), ( , 0)		  
C. vertices: ( -7, 0), ( 7, 0)
foci: (- , 0), ( , 0)		  
D. vertices: (0, -10), (0, 10)
foci: (0, – ), (0, )		  

Question 7 of 20
 5.0/ 5.0 Points
Write the equation in terms of a rotated x’y’-system using θ, the angle of rotation. Write the equation involving x’ and y’ in standard form. xy +16 = 0; θ = 45°
A. +  = 1  
B. y‘2 = -32x’  
C. + = 1  
D. – = 1  

Question 8 of 20
 0.0/ 5.0 Points
Write the appropriate rotation formulas so that in a rotated system the equation has no x’y’-term.

10x2 – 4xy + 6y2– 8x + 8y = 0
A. x = -y’; y = x’  
B. x = x’ – y’; y = x’ + y’  
C. x = (x’ – y’); y = (x’ + y’)  
D. x = x’ – y’; y = x’ + y’  

Question 9 of 20
 0.0/ 5.0 Points
Find the location of the center, vertices, and foci for the hyperbola described by the equation.

– = 1
A. Center: ( -4, 1); Vertices: ( -10, 1) and ( 2, 1); Foci: and
(		  
B. Center: ( -4, 1); Vertices: ( -9, 1) and ( 3, 1); Foci: ( -3 + , 2) and ( 2 + , 2)  
C. Center: ( -4, 1); Vertices: ( -10, -1) and ( 2, -1); Foci: ( -4 – , -1) and ( -4 + , -1)  
D. Center: ( 4, -1); Vertices: ( -2, -1) and ( 10, -1); Foci: and  

Question 10 of 20
 0.0/ 5.0 Points
Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation’s domain and range.

x = 2t, y = t2+ t + 3
A. Domain: (-∞, ∞); Range: -1x, ∞)

  
B. Domain: (-∞, ∞); Range: [ 2.75, ∞)

  
C. Domain: (-∞, ∞); Range: [ 3, ∞)
  
D. Domain: (-∞, ∞); Range: [ 2.75, ∞)
  

Question 11 of 20
 0.0/ 5.0 Points
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.

y = ±
A. Asymptotes: y = ± x
  
B. Asymptotes: y = ± x

  
C. Asymptotes: y = ± x
  
D. Asymptotes: y = ± x
  

Question 12 of 20
 0.0/ 5.0 Points
Graph the ellipse.

16(x – 1)2 + 9(y + 2)2= 144
A.  
B.  
C.  
D.  

Question 13 of 20
 0.0/ 5.0 Points
Is the relation a function?

y = x2+ 12x + 31
A. Yes  
B. No  

Question 14 of 20
 5.0/ 5.0 Points
Determine the direction in which the parabola opens, and the vertex.

y2= + 6x + 14
A. Opens upward; ( -3, 5)  
B. Opens upward; ( 3, 5)  
C. Opens to the right; ( 5, 3)  
D. Opens to the right; ( 5, -3)  

Question 15 of 20
 0.0/ 5.0 Points
Match the equation to the graph.

x2= 7y
A.  
B.  
C.  
D.  

Question 16 of 20
 0.0/ 5.0 Points
y2= -2x
A.  
B.  
C.  
D.  

Question 17 of 20
 0.0/ 5.0 Points
Convert the equation to the standard form for a hyperbola by completing the square on x and y.

x2 – y2+ 6x – 4y + 4 = 0
A. (x + 3)2 + (y + 2)2 = 1  
B. – = 1  
C. (x + 3)2 – (y + 2)2 = 1  
D. (y + 3)2– (x + 2)2 = 1  

Question 18 of 20
 0.0/ 5.0 Points
Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.

x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π
A. x2 – y2 = 6; -6 ≤ x ≤ 6  
B. x2 – y2 = 36; -6 ≤ x ≤ 6  
C. x2 + y2 = 6; -6 ≤ x ≤ 6  
D. x2 + y2 = 36; -6 ≤ x ≤ 6  

Question 19 of 20
 5.0/ 5.0 Points
Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.

y2+ 2y – 2x – 3 = 0
A. (y + 1)2 = 2(x + 2)  
B. (y – 1)2 = -2(x + 2)  
C. (y + 1)2 = 2(x – 2)  
D. (y – 1)2 = 2(x + 2)  

Question 20 of 20
 0.0/ 5.0 Points
Convert the equation to the standard form for a hyperbola by completing the square on x and y.

y2 – 25x2+ 4y + 50x – 46 = 0
A. – (x – 2)2 = 1  
B. – (y – 1)2 = 1  
C. (x – 1)2 – = 1  
D. – (x – 1)2 = 1  

Complete all 7 steps. Place work and answers, below each respective step. Expand the space as needed. 2. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit

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1.       Complete all 7 steps. Place work and answers, below each respective step. Expand the space as needed.

2.       Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.

3.       Word-process formulas using Equation Editor and diagrams using Drawing Tool.

 

 

Problem 1

Given y = f(x) = x2 + 2x +3

a)      Use the definitional formula given below to find the derivative of the function.

 

b)      Find the value of the derivative at x = 3.

 

 

Problem 2

Given, y = f(x) = 2 x3 – 3x2 + 4x +5

a)      Use the Power function to find derivative of the function.

b)      Find the value of the derivative at x = 4.

 

 

Problem 3

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.

R(x) = 16x – x2

C(x) = 20 + 4x

a)      Determine the profit function P(x).

b)      Use Excel to graph the functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.

c)       Compute the break-even quantities.

d)      Determine the average cost at the break-even quantities.

e)      Determine the marginal revenue R’(x).

f)       Determine the marginal cost C’(x)

g)      At what quantity is the profit maximized?

MATH UNIT 3

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This Discussion topic has multiple parts. Please read and give a thorough response to each part. 

Original Post

1. Write and post a real world word problem that can be solved using a linear equation in one variable. All of the information necessary to solve the equation must be included in your problem. For examples of such problems, see Exercises 29-48 in Section 6.4 on pages 318 and 319 of your textbook. Feel free to use one of these problems as a model, but you must change names, numbers, details, etc. to make the problem your own… 

2. Use the Procedure To Solve a Word Problem given in Section 6.4 on page 315 of your textbook to write a complete solution to your problem. You only need to complete steps 1 through 6. You do not need to check your solution. See Example 1 on page 315 and use it as a guide. 

Note: there is a very helpful example in Doc Sharing on how to take an example and build a similar one to it to use in your post.    

Example: A rug cleaning service charges a flat fee of $35.00 and a per room fee of $28.00. If the Morgan’s bill was $175 before taxes, how many rooms did they have cleaned?

You are being asked to find the number of rooms that were cleaned. 
Let r = the number of rooms being cleaned. 
If r is the number of rooms being cleaned, then $28.00r would be the cost of cleaning r rooms. 
Flat fee + cost of cleaning r rooms = total bill 
                                       $35 + $28r = $175
Now solve the equation. 
                                            35 + 28r = 175
                                    35 – 35 + 28r = 175 – 35
                                                     28r = 140 
                                                          r = 5

Since r is the number of rooms that were cleaned, you know that the Morgan’s had the rugs in 5 rooms cleaned.

First Response to a Classmate

3. Find a classmate’s problem and solution that has NOT already been checked by a classmate. Show all steps in your check and explain each step as you go. Example 1 on page 315 is one example of a thorough check. If the classmate’s equation does not check, tactfully let the classmate know. 

Example: The total bill is the flat fee plus the per room charge. Total bill = flat fee + per room charge 
……. = $35 + $28(5)
……. = 35 + 140 
……. = $175

The solution to the problem checks.

Second Response to a Classmate

4. Find at least one other post to comment on. Make sure your comments are substantive and advance the Discussion. Do not check a second classmate’s equation. Each of your classmates will also need to check a problem. You can look for opportunities to help another student, give advice on solving a problem a different way, or offer any other substantive comment. 

STUDENT 1

 
 

Leo works in the sales department of a gaming company earning a salary of $800 per week. He also receives a 12% commission on the total amount of sales he makes. What must his total sales be in a week if he is to make a total of $1248?

Must find the total amount of sales made that week.

Total amount of sales for the week.  Sales = s

$800 + 12%(s) = $1248

800 + .12s = 1248

800 – 800 + .12s = 1248 – 800

.12s = 448

.12s/.12 = 448/.12

= 3733.33

Total Sales = $3,733.33

STUDENT 2
Flea Market Candles by Barbara

Barbara is selling homemaid candles at the local flea market. Determine the cost of a Jar candle before tax if the total cost is $16.50, including a 10% tax.

Let C=cost of the candle before tax

Then 0.10=10% of the cost before tax

Cost of the candle before tax + tax on the candle=16.50

c+0.10c=16.50

1.10c=16.50

1.10/1.10c=16.50/1.10

c=15.00

Therefore the candle cost 15.00 before sales tax.

 

 

Harry Potter and the Sorcerer’s Stone by J.K. Rowling

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As with most literary works, there are recurrent universal patterns in Harry Potter and the Sorcerer’s Stone. Consider the definition of Mythological Criticism:

    A central concept in mythological criticism is the archetype, a symbol, character, situation, or image that evokes a deep universal response. The idea of the archetype came into literary criticism from the Swiss psychologist Carl Jung. Jung believed that all individuals share a “collective unconscious,” a set of primal memories common to the human race, existing below each person’s conscious mind. Critic Joseph Campbell identified archetypal symbols and situations in literary works by demonstrated how similar mythic characters appear in virtually every culture on every continent.

For your 1000 word written analysis, you will track the progress of Harry Potter as a Hero Archetype. Please follow our Hero’s Quest Outline and fill in ALL 12 story steps (as listed below). There are no “right” answers to this assignment – follow your instincts and describe what you deem important and necessary!

You will need to write specific examples of Harry’s hero quest, so keep a pen and pad handy as you read the novel. Please refer to specific scenes, characters, events, changes of consciousness and/or circumstance. Please include at least five (5) quotes with page numbers!

As you venture through the novel, think about what makes Harry a hero: How does his special world compare to his ordinary world? What actions can be deemed heroic? Who are Harry’s teachers and guides? What is his quest? Does his quest change during the course of the novel? Who are his allies or enemies? What challenges or conflicts does Harry need to overcome? How does Harry fit the hero archetype?

Your grade will be based on the thoroughness of your analysis (if you successfully respond to all 12 story steps!), the strength of your quotes/examples, and your thoughtfulness and openmindedness! You may write more than the 1000 word minimum, but please keep your analysis under 1,500 words! Please write in paragraph form – do not post an outline!

To receive maximum credit, please post your analysis via our Turnitin link on our Moodle course page page PRIOR to the whole-class forum discussion. Good luck and enjoy!

************************************************************************************************

12 Story Steps To The Myth — Please Respond to All 12!!!

Act One

(1) Ordinary World – Something is missing in this world. It’s the hero or hera’s present, everyday situation. It’s described in order to create a contrast. A question is raised.

(2) Call To Adventure – information is put into the hero or hera’s system, often brought by a messenger.

(3) Reluctant Hero or Hera

(4) Wise Old Person (most optional of steps) – Maybe gives message to trust the path.

Act Two

(5) Special World – Hero gets very committed by his will – or not.

(6) Tests, Allies & Enemies – Enmities and alliances are formed. What are the conditions to the quest? How will the hero react?

(7) Innermost Cave – Holds what the hero wants.

(8) Supreme Ordeal (at ¾ point in 2nd Act) – Hero surviving/transcending “death.”

(9) Seizing The Sword – Taking possession. Enjoying the spoils. But maybe something else chases the hero. Often a missing piece is introduced.

Act Three

(10) The Road Back

(11) Resurrection – Another hero’s test. Final proof – better if visual.

(12) Return with Elixir – To share with everyone.

FIN 534 Midterm Exam

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1. Which of the following statements is CORRECT?

2. You are considering two equally risky annuities, each of which pays $25,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

3. Which of the following statements is CORRECT?

4. A $150,000 loan is to be amortized over 6 years, with annual end-of-year payments. Which of these statements is CORRECT?

5. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?

6. Your bank offers a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. If you invest $2,000 in the CD, how much will you have when it matures?

7. Of the following investments, which would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.

8. Ellen now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

9. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 8% is CORRECT?

10. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?

11. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment?

12. Which of the following statements is CORRECT?

13. You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

14. Which of the following statements is CORRECT?

15. How much would Roderick have after 6 years if he has $500 now and leaves it invested at 5.5% with annual compounding?

16. Which of the following statements is CORRECT?

17. A Treasury bond has an 8% annual coupon and a 7.5% yield to maturity. Which of the following statements is CORRECT?

18. Which of the following statements is CORRECT?

19. Assume that interest rates on 15-year noncallable Treasury and corporate bonds with different ratings are as follows:

20. A 10-year bond pays an annual coupon, its YTM is 8%, and it currently trades at a premium. Which of the following statements is CORRECT?

21. Which of the following statements is NOT CORRECT?

22. Which of the following statements is NOT CORRECT?

23. A 15-year bond has an annual coupon rate of 8%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 6%. Which of the following statements is CORRECT?

24. An 8-year Treasury bond has a 10% coupon, and a 10-year Treasury bond has an 8% coupon. Both bonds have the same yield to maturity. If the yield to maturity of both bonds increases by the same amount, which of the following statements would be CORRECT?

25. Which of the following statements is CORRECT?

26. Bond A has a 9% annual coupon while Bond B has a 6% annual coupon. Both bonds have a 7% yield to maturity, and the YTM is expected to remain constant. Which of the following statements is CORRECT?

27. A 10-year bond with a 9% annual coupon has a yield to maturity of 8%. Which of the following statements is CORRECT?

28. Which of the following events would make it more likely that a company would choose to call its outstanding callable bonds?

29. If its yield to maturity declined by 1%, which of the following bonds would have the largest percentage increase in value?

30. Which of the following statements is CORRECT?

 

 

 

stat 200

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STAT200 : Introduction to Statistics Final Examination, Page 1 of 6

STAT 200

OL4 / OL2 Sections

Final Exam

 

This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.

Answer all 30 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted.

Record your answers and work on the separate answer sheet provided.

This exam has 300 total points.

You must include the Honor Pledge on the title page of your submitted final exam. Exams submitted without the Honor Pledge will not be accepted.

1. True or False. Justify for full credit. (25 pts)

(a) If there is no linear correlation between two variables, then these two variables are not related in any way.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 2 of 6

(b) If the variance from a data set is zero, then all the observations in this data set are identical.

(c) .ofcomplementtheis where,1)( AAAandAP 

(d) In a hypothesis testing, if the P-value is less than the significance level α, we reject the null hypothesis.

(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.

Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes) Frequency

1.0 – 1.9 2

2.0 – 2.9 12

3.0 – 3.9 2

4.0 – 4.9 4

2. What percentage of the checkout times was less than 3 minutes? (5 pts)

3. In what class interval must the median lie? Explain your answer. (5 pts)

4. Calculate the mean of this frequency distribution. (5 pts)

5. Calculate the standard deviation of this frequency distribution. (Round the answer to two decimal places) (10 pts)

Refer to the following data to answer questions 6, 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

2 15 15 18 40

6. Find the sample standard deviation. (Round the answer to two decimal places) (10 pts)

7. Find the coefficient of variation. (5 pts)

8. Are any of these study times considered unusual based on the Range Rule of Thumb?

Show work and explain. (5 pts)

Refer to the following information for Questions 9, 10 and 11. Show all work. Just the answer, without supporting work, will receive no credit.

Consider selecting one card at a time from a 52-card deck. Let event A be the first card is an ace, and event B be the second card is an ace. (Note: There are 4 aces in a deck of cards)

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 3 of 6

9. If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (10 pts) 10. If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? (Express the answer in simplest fraction form) (10 pts)

11. Are A and B independent when the selection is with replacement? Why or why not? (5 pts)

Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

12. What is the probability that a randomly selected junior is taking at least one of these two courses? (10 pts)

13. What is the probability that a randomly selected junior is taking PSYC300, given that

he/she is taking STAT200? (10 pts)

14. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10 qualified candidates. How many different ways can the officers be appointed? (5 pts)

15. Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the seven

books with her in a road trip. How many different ways can the three books be selected? (5 pts)

Questions 16 and 17 involve the random variable x with probability distribution given below. Show all work. Just the answer, without supporting work, will receive no credit.

x -1 0 1 2

()Px 0.1 0.3 0.4 0.2

16. Determine the expected value of x. (5 pts)

17. Determine the standard deviation of x. (Round the answer to two decimal places) (10 pts)

Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 8 times.

18. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and

probability of failures (q), respectively? (5 pts)

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 4 of 6

19. Find the probability that that she returns at least 1 of the 8 serves from her opponent. (10 pts)

20. How many serves can she expect to return? (5 pts)

Refer to the following information for Questions 21, 22, and 23. Show all work. Just the answer, without supporting work, will receive no credit.

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.

21. What is the probability that a randomly selected dogwood tree is greater than 12 feet? (5 pts)

22. Find the 75th percentile of the dogwood tree height distribution. (10 pts)

23. If a random sample of 36 dogwood trees is selected, what is the probability that the mean height

of this sample is less than 10 feet? (10 pts)

24. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will

receive no credit. (15 pts)

25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100, we perform the following hypothesis test at the 0.05

 level.

750:

750:

1

0

H

H

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the critical values. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(c) What is your conclusion of the test? Please explain. (20 pts)

26. Consider the hypothesis test given by

5.0:

5.0:

1

0

pH

pH

In a random sample of 225 subjects, the sample proportion is found to be 51.0ˆ p .

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 5 of 6

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of 0

H at the 0.01

 level?

Explain. (20 pts)

27. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table.

Number of Words Recalled

Subject 1 hour later 24 hours later

1 14 12

2 18 15 3 11 9

4 13 12

5 12 12

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours?

Assume we want to use a 0.01 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion.

(20 pts)

Refer to the following data for Questions 28 and 29.

x 0 -1 3 5 y 3 -2 3 8

28. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. (15 pts)

29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work and justify your answer. (5 pts)

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 6 of 6

30. The UMUC MiniMart sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 100 purchases yields observed counts 30, 24, 22, and 24 for types 1, 2, 3, and 4, respectively.

Type 1 2 3 4

Number 30 24 22 24

Assume we want to use a 0.10 significance level to test the claim that the four types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the four types are

equally popular? Justify your answer. (20 pts)

Write a response to this classmate’s post “I NEED THIS ON 05/18/18 BY 11:59PM”

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In what ways is it important to view a biblical worldview as affecting your desires?              

A biblical worldview is depended upon the plans God has for my life, verses my own desires, for instance, I may want to be rich, but God may just want me to be comfortable. Therefore, it’s so important that we seek him first before making any decisions and scripture already tells us,”11For I know the plans I have for you,”declares the Lord,”plans to prosper you and not to harm you, plans to give you hope and a future.”(Jeremiah 29:11, NIV) It’s also important to view bibical so, that we know and understand God’s thoughts towards us, this way we are in alignment with our purpose.

Have you ever experienced a conflict between what you know and what you desire?    

          

I remember earlier in my relationship with God, there was a time when I would war in my spirit knowing the right thing to do, but my desire was pulling me towards the wrong thing. My conflict was me wanting to go to a club every weekend to be with my friends because this is what I enjoyed doing often. However, the more my relationship grew with Christ, the more my flesh still wanted to hangout, I would tell myself it’s not too bad if you go oneday instead of three.Oneday, I was driving to pick up a couple of my friends and this time it was different for me, we got to the club and I let them out, but I could not go in, after they went in I sat in the car crying to the extreme.At that point, I knew immediately there is no more straddling the fence and there needed to be a decision made.Scripture says,”I know all the things you do, that you are neither hot nor cold.I wish that you were one or the other! (Revelation 3:15, NLT) 

Examine some potential pitfalls in your worldview or even the worldview you see upheld around you. How would you propose overcoming it?            

  

We say that all men are created equal, but it’s not true because, history show that we are seperated by culture, race, and gender. It seems as though the more money you have, the more power you have. There is so much disrespect between one another, to the point whereas to, whatever comes out the mouth it is said, without a second thought.We can elect more politicians that has a heart for the people, also standing together on different laws that will work for everyone, not just for the ones that are powerful because of money and /or that have authority. 

Statistics Exam 2

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Question 1 (3.33 points) Question 1 Unsaved

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

 

n = 87, x = 48; 98 percent

Question 1 options:

 

0.447 < p < 0.657

0.428 < p < 0.676

0.448 < p < 0.656

0.427 < p < 0.677

 

 

 

Save

Question 2 (3.33 points) Question 2 Unsaved

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.

 

n = 12, sample mean (x-bar) = 26.8, s = 6.8, 99 percent

Question 2 options:

 

20.70 < μ < 32.90

 

20.72 < μ < 32.88

 

21.46 < μ < 32.14

 

20.58 < μ < 33.02

Save

Question 3 (3.33 points) Question 3 Unsaved

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

 

n = 144, x = 82; 90 percent

Question 3 options:

 

0.501 < p < 0.637

 

0.505 < p < 0.633

 

0.503 < p < 0.635

 

0.500 < p < 0.638

 

Save

Question 4 (3.33 points) Question 4 Unsaved

Solve the problem.

 

The following confidence interval is obtained for a population proportion, p:

(0.293, 0.317)

Use these confidence interval limits to find the margin of error, E.

Question 4 options:

 

0.010

 

0.013

 

0.024

 

0.012

Save

 

Question 5 (3.33 points) Question 5 Unsaved

Solve the problem.

 

Find the value of -zα/2 that corresponds to a level of confidence of 96.68 percent.

Question 5 options:

 

0.0166

 

-1.84

 

2.13

 

-2.13

Save

 

Question 6 (3.33 points) Question 6 Unsaved

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

 

Of 89 adults selected randomly from one town, 67 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance.

Question 6 options:

 

0.663 < p < 0.842

 

0.635 < p < 0.871

 

0.678 < p < 0.828

 

0.646 < p < 0.859

Save

 

 

Question 7 (3.33 points) Question 7 Unsaved

Use the confidence level and sample data to find a confidence interval for estimating the population μ.

 

A random sample of 100 full-grown lobsters had a mean weight of 22 ounces and a standard deviation of 3.7 ounces. Construct a 98 percent confidence interval for the population mean μ.

Question 7 options:

 

20 < μ < 22

 

21 < μ < 23

 

21 < μ < 24

 

22 < μ < 24

Save

 

 

Question 8 (3.33 points) Question 8 Unsaved

Solve the problem.

 

The following confidence interval is obtained for a population proportion, p:

(0.870, 0.894)

Use these confidence interval limits to find the point estimate, (p-bar) .

Question 8 options:

 

0.882

 

0.885

 

0.870

 

0.894

Save

Question 9 (3.33 points) Question 9 Unsaved

Use the confidence level and sample data to find the margin of error E.

 

The duration of telephone calls directed by a local telephone company: population standard deviation = 3.0 minutes, n = 580, 97 percent confidence.

Question 9 options:

 

0.057 minutes

 

0.011 minutes

 

0.270 minutes

 

0.006 minutes

Save

Question 10 (3.33 points) Question 10 Unsaved

Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (μ, p, σ )for the indicated parameter.

 

A researcher claims that 62% of voters favor gun control.

Question 10 options:

 

H0: p < 0.62

H1: p ≥ 0.62

 

H0: p ≥ 0.62

H1: p < 0.62

 

H0: p = 0.62

H1: p ≠ 0.62

 

H0: p ≠ 0.62

H1: p = 0.62

Save

Question 11 (3.33 points) Question 11 Unsaved

Find the P-value for the indicated hypothesis test.

 

In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

Question 11 options:

 

0.0048

 

0.0262

 

0.0024

 

0.0524

Save

 

Question 12 (3.33 points) Question 12 Unsaved

Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (μ, p, σ )for the indicated parameter.

 

An entomologist writes an article in a scientific journal which claims that fewer than 12 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

Question 12 options:

 

H0: p = 0.0012

H1: p > 0.0012

 

H0: p > 0.0012

H1: p ≤ 0.0012

 

H0: p = 0.0012

H1: p < 0.0012

 

H0: p < 0.0012

H1: p ≥ 0.0012

Save

Question 13 (3.33 points) Question 13 Unsaved

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

 

The owner of a football team claims that the average attendance at games is over 794, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

Question 13 options:

 

There is sufficient evidence to support the claim that the mean attendance is less than 794.

 

There is not sufficient evidence to support the claim that the mean attendance is greater than 794.

 

There is not sufficient evidence to support the claim that the mean attendance is less than 794.

 

There is sufficient evidence to support the claim that the mean attendance is greater than than 794.

Save

 

Question 14 (3.33 points) Question 14 Unsaved

Find the P-value for the indicated hypothesis test.

 

In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.

Question 14 options:

 

0.2843

 

0.2157

 

-0.2843

 

0.5686

Save

 

 

Question 15 (3.33 points) Question 15 Unsaved

Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (μ, p, σ )for the indicated parameter.

 

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.

Question 15 options:

 

H0: μ = 14

H1: μ > 14

 

H0: μ < 14

H1: μ ≥ 14

 

H0: μ > 14

H1: μ ≤ 14

 

H0: μ = 14

H1: μ < 14

Save

Question 16 (3.33 points) Question 16 Unsaved

Use the given information to find the P-value.

 

The test statistic in a left-tailed test is z = -2.05.

Question 16 options:

 

0.0453

 

0.0202

 

0.5000

 

0.4798

 

Save

Question 17 (3.33 points) Question 17 Unsaved

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

 

An entomologist writes an article in a scientific journal which claims that fewer than 18 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Question 17 options:

 

There is not sufficient evidence to support the claim that the true proportion is less than 18 in ten thousand.

 

There is sufficient evidence to support the claim that the true proportion is greater than 18 in ten thousand.

 

There is sufficient evidence to support the claim that the true proportion is less than 18 in ten thousand.

 

There is not sufficient evidence to support the claim that the true proportion is greater than 18 in ten thousand.

Save

Question 18 (3.33 points) Question 18 Unsaved

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

 

α = 0.1 for a two-tailed test.

Question 18 options:

 

±1.645

 

±1.4805

 

±2.33

 

±2.052

Save

Question 19 (3.33 points) Question 19 Unsaved

Determine whether the samples are independent or consist of matched pairs.

 

The effect of caffeine as an ingredient is tested with a sample of regular soda and another sample with decaffeinated soda.

Question 19 options:

 

Matched pairs

 

Independent samples

 

Save

 

Question 20 (3.33 points) Question 20 Unsaved

The two data sets are dependent. Find the average deviation (d-bar) to the nearest tenth.

A: 52 55 60 63 51

B: 29 25 20 25 22

 

 

Question 20 options:

 

41.6

 

32.0

 

40.0

 

19.2

Save

Question 21 (3.33 points) Question 21 Unsaved

Find sd.

 

The differences between two sets of dependent data are 0.42 0.26 0.26 0.3 0.28. Round to the nearest hundredth.

Question 21 options:

 

0.11

 

0.07

 

0.21

 

0.04

Save

 

Question 22 (3.33 points) Question 22 Unsaved

Find sd.

 

The differences between two sets of dependent data are -9 3 -9 6. Round to the nearest tenth.

Question 22 options:

 

181.7

 

7.9

 

4.0

 

6.3

Save

 

Question 23 (3.33 points) Question 23 Unsaved

Find sd.

 

The differences between two sets of dependent data are -8 -9 -9 -6 -7. Round to the nearest tenth.

Question 23 options:

 

1.3

 

2.6

 

1.7

 

1.0

Save

 

Question 24 (3.33 points) Question 24 Unsaved

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.

 

We wish to compare the means of two populations using paired observations. Suppose that d-bar = 3.125, Sd = 2.911, and n = 8, and that you wish to test the following hypothesis at the 1 percent level of significance:

 

H0: μd = 0 against H1: μd > 0.

 

What decision rule would you use?

Question 24 options:

 

Reject H0 if test statistic is greater than 2.998.

 

Reject H0 if test statistic is less than 2.998.

 

Reject H0 if test statistic is greater than -2.998.

 

Reject H0 if test statistic is greater than -2.998 and less than 2.998.

Save

 

Question 25 (3.33 points) Question 25 Unsaved

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μd = 0. Compute the value of the t test statistic.

 

A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below.

Plot: 1 2 3 4 5 6 7 8 9 10 

Before 9 9 8 7 6 8 5 9 10 11

After 10 9 9 8 7 10 6 10 10 12

You wish to test the following hypothesis at the 10 percent level of significance.

 

Ho: μD = 0 against H1: μD ≠ 0.

 

What is the value of the appropriate test statistic?

Question 25 options:

 

2.536

 

2.033

 

5.014

 

1.584

Save

 

Question 26 (3.43 points) Question 26 Unsaved

Find the required χ2-value.

 

For a χ2-curve with 7 degrees of freedom, find the χ2-value having area 0.05 to its right.

Question 26 options:

 

15.507

 

14.067

 

3.325

 

2.167

Save

 

Question 27 (3.33 points) Question 27 Unsaved

Find the required χ2-value.

 

For a χ2-curve with 24 degrees of freedom, find  .

Question 27 options:

 

13.848

 

12.401

 

36.415

 

13.091

Save

 

Question 28 (3.33 points) Question 28 Unsaved

Find the required χ2-value.

 

For a χ2-curve with 12 degrees of freedom, find  .

Question 28 options:

 

23.336

 

19.675

 

21.026

 

5.226

Save

Question 29 (3.33 points) Question 29 Unsaved

Find the value of the chi-square test statistic for the goodness-of-fit test.

 

You wish to test the claim that workplace accidents are distributed on workdays as follows:      In a study of 100 workplace accidents, 27 occurred on a Monday, 13 occurred on a Tuesday, 15 occurred on a Wednesday, 13 occurred on a Thursday, and 32 occurred on a Friday. What is the value of the χ2 test statistic? The observed frequencies and the expected frequencies are shown below.

 

 

Question 29 options:

 

χ2 = 2.286

 

χ2 = 5.333

 

χ2 = 0.889

 

χ2 = 0.827

Save

 

Question 30 (3.33 points) Question 30 Unsaved

Group the bivariate data into a contingency table.

 

The table below provides data on sex, political party affiliation, and income bracket for a sample of people questioned during a poll. Group the bivariate data for the two variables “sex” and “political party” into a contingency table.

 

 

M Rep High

F Dem Middle

F Dem Middle

M Dem Low

F Other Middle 

M Rep Low

F Rep High

M Rep High

M Dem High

F Rep Low

M Dem High 

F Rep Middle

F Dem Middle

M Dem Middle

M Rep Low

F Dem High 

M Rep Low

F Other High 

M Other Middle 

F Dem Low

M Dem Middle

M Rep Low

F Dem Middle

Question 30 options: