week 8 review

/in /by
1.

Write the following set in builder notation form

2.
Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9

y = x +

 


y = x –

 


y = –x –

 


y = –x +

 

3.

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

one and only one solution


one and only one solution


one and only one solution


infinitely many solutions

4.
Find the present value of $40,000 due in 4 years at the given rate of interest 8%/year compounded monthly.

5.
Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 4 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.

6.

Find the pivot element to be used in the next iteration of the simplex method.

7.

Indicate whether the matrix is in row-reduced form.

8.

In a poll conducted among 180 active investors, it was found that 100 use discount brokers, 122 use full-service brokers, and 54 use both discount and full-service brokers. How many investors use only discount brokers?

9.
If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?

10.
Find the simple interest on a $400 investment made for 5 years at an interest rate of 7%/year. What is the accumulated amount?

11.

Metro Department Store’s annual sales (in millions of dollars) during 5 years were

Annual Sales, y

5.8

6.1

7.2

8.3

9

Year, x

1

2

3

4

5

Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.




12.

The following breakdown of a total of 18,686 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT).

Mode of Transportation

Car

Train

Bicycle

Plane

Number of Fatalities

16,525

842

698

538

What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.

13.
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.

14.

Use Venn diagrams to illustrate the statement.

15.
A survey of 900 subscribers to the Los Angeles Times revealed that 700 people subscribe to the daily morning edition and 400 subscribe to both the daily and the Sunday editions.How many subscribe to the Sunday edition?

16.

Solve the linear programming problem by the simplex method.

17.

Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

18.

Maximize

P= 10x + 12y

subject to

19.

Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.

20.

Let .

Are the events F and G mutually exclusive?

21.

Solve the system of linear equations using the Gauss-Jordan elimination method.

22.

Solve the linear system of equations

Unique solution:


Unique solution:


Infinitely many solutions:

23.
If a merchant deposits $1,500 annually at the end of each tax year in an IRA account paying interest at the rate of 10%/year compounded annually, how much will she have in her account at the end of 25 years? Round your answer to two decimal places.

24.
An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event “A head is tossed and an odd number is rolled.”

25.
What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?

week 4 midterm

/in /by
1.
Find an equation of the line that passes through the points (1, 4) and ( -7, -4)

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.

3.

Solve the linear system of equations

Unique solution:


Unique solution:


Infinitely many solutions:


4.

Consider the linear programming problem.

Sketch the feasible set for the linear programming problem.
5.

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

one and only one solution


one and only one solution


one and only one solution


infinitely many solutions


6.

Indicate whether the matrix is in row-reduced form.

7.

Find the pivot element to be used in the next iteration of the simplex method.

8.

Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.

9.
Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9

y = x +

 


y = x –

 


y = –x –

 


y = –x +

10 If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?


11.

Maximize

P= 10x + 12y

subject to

12.

Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

13.

Find the slope of the line that passes through the given pair of points.

(2, 2) and (8, 5)

14.

Consider the linear programming problem.

Sketch the feasible set for the linear programming problem.

15.

Solve the system of linear equations using the Gauss-Jordan elimination method.

16.

Solve the linear system of equations

Unique solution:


Unique solution:


Infinitely many solutions:


17.

Determine whether the given simplex table is in the final form. If so, find the solution to the associated regular linear programming problem.

18.

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.


 
 
 
 
 
19.

Solve the linear programming problem by the simplex method.

 
20.

Metro Department Store’s annual sales (in millions of dollars) during 5 years were

Annual Sales, y

5.8

6.1

7.2

8.3

9

Year, x

1

2

3

4

5

Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.



 

21.

Solve the linear system of equations

Unique solution:


Unique solution:


Infinitely many solutions:

22.

Solve the system of linear equations using the Gauss-Jordan elimination method.

23.

Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.

24.

Solve the system of linear equations, using the Gauss-Jordan elimination method.

25.

Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope – 1.
 
 
 
 
 

MAT 540 Quiz 4

/in /by

MAT 540Week 6 Quiz 4:

 

 

1. The standard form for the computer solution of a linear programming problem requires all variables to the right and all numerical values to the left of the inequality or equality sign 

True/ False

 

2. _________ is maximized in the objective function by subtracting cost from revenue.

Profit

 Revenue

 Cost

 Productivity

 

3. A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today’s production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit?

$380

 $400

 $420

 $440

 $480

 

4. In an unbalanced transportation model, supply does not equal demand and supply constraints have signs.   True/ False

 

5. The production manager for Liquor etc. produces 2 kinds of beer: light and dark. Two of his resources are constrained: malt, of which he can get at most 4800 oz per week; and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the objective function?

Z = $1L + $2D

 Z = $4L + $8D

 Z = $12L + $8D

 Z = $2L + $1D

 Z = $2L + $4D

 

6. In a media selection problem, the estimated number of customers reached by a given media would generally be specified in the _________________. Even if these media exposure estimates are correct, using media exposure as a surrogate does not lead to maximization of___.

problem constraints, sales

 problem constraints, profits

 objective function, profits

 problem output, marginal revenue

 problem statement, revenue

 

7. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50. Which of the following is not a feasible production combination?

 0L and 0V

 0L and 1000V

 1000L and 0V

 0L and 1200V

 

8. When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell.   True/ False

 

9. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.      True/ False

 

10. In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure.  True/ False

 

11. ____________ solutions are ones that satisfy all the constraints simultaneously.

alternate

 feasible

 infeasible

 optimal

 unbounded

 

12. The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit?

$220

 $270

 $320

 $420

 $520

 

13. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.   True/ False

 

14. When using linear programming model to solve the “diet” problem, the objective is generally to maximize profit.   True/ False

 

15. Profit is maximized in the objective function by

subtracting cost from revenue

 subtracting revenue from cost

 adding revenue to cost

 multiplying revenue by cost

 

16. Linear programming model of a media selection problem is used to determine the relative value of each advertising media.    True/ False

 

17. Media selection is an important decision that advertisers have to make. In most media selection decisions, the objective of the decision maker is to minimize cost.   True/ False

 

18. The dietician for the local hospital is trying to control the calorie intake of the heart surgery patients. Tonight’s dinner menu could consist of the following food items: chicken, lasagna, pudding, salad, mashed potatoes and jello. The calories per serving for each of these items are as follows: chicken (600), lasagna (700), pudding (300), salad (200), mashed potatoes with gravy (400) and jello (200). If the maximum calorie intake has to be limited to 1200 calories. What is the dinner menu that would result in the highest calorie in take without going over  the total calorie limit of 1200.

chicken, mashed potatoes and gravy, jello and salad

 lasagna, mashed potatoes and gravy, and jello

 chicken, mashed potatoes and gravy, and pudding

 lasagna, mashed potatoes and gravy, and salad

 chicken, mashed potatoes and gravy, and salad

 

19. In a multi-period scheduling problem the production constraint usually takes the form of :

beginning inventory + demand – production = ending inventory

 beginning inventory – demand + production = ending inventory

 beginning inventory – ending inventory + demand = production

 beginning inventory – production – ending inventory = demand

 beginning inventory + demand + production = ending inventory

 

20. A constraint for a linear programming problem can never have a zero as its right-hand-side value.   True/ False

 

 

 

Help

/in /by

Discrete Probability Distribution ???

   Imagine you are in a game show, where

Now, let us start the money give-away!  There are 4 prizes hidden on a game board with 16 spaces.  One prize is worth $4000, another is worth $1500, and two are worth $1000.

But, wait!!!  You are also told that, in the rest of the spaces, there will be a bill of $50 that you have to pay to the host as a penalty for not making the “wise” choice.

OK, you are lucky that you only have to pay $50 for making a bad choice.  Imagine that you failed to answer the question asked by

in the Monty Python and the Holy Grail!

But, of course, it is a much kinder and gentler world now than the time of King Arthur and his knights.

monty-python-holy-grail-clip-clop-300w.jpg

  In this modern game show, you are actually given a choice, a real choice.

Choice #1:  You are offered a sure prize of $400 cash, and you just take the money and walk away.  Period.  No question asked…..

Choice #2:  Take your chance and play the game…….

What would be your choice?  Take the money and run, or play the game?  Why???Hmmmm…….

   You have to make a decision…… quick ……

 

MAT540 Quiz 3

/in /by

Quiz 3

Question 1 

  Surplus variables are only associated with minimization problems. 

 

 Question 2 

  A feasible solution violates at least one of the constraints. 

  

 Question 3 

  A linear programming model consists of only decision variables and constraints. 

 

 Question 4 

  Graphical solutions to linear programming problems have an infinite number of possible objective function lines. 

 

 Question 5  

  If the objective function is parallel to a constraint, the constraint is infeasible. 

  

 Question 6 

  A linear programming problem may have more than one set of solutions. 

 

 Question 7 

  In minimization LP problems the feasible region is always below the resource constraints.

Question 8  

  The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.  This linear programming problem is a:

  

 Question 9  

  The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.  The equation for constraint DH is:

  

 Question 10  

  The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.  Which of the following constraints has a surplus greater than 0?

  

 Question 11 

  Which of the following statements is not true?

  

 Question 12  

  Decision variables

Question 13  

  The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

 

 Question 14  

  The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the objective function?

 

 Question 15  

  The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

 

 Question 16  

  Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function?

  

 Question 17  

  Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

 

 Question 18  

  A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.  What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation. 

  

 Question 19  

  Solve the following graphicallyMax z = 3×1 +4×2 s.t. x1 + 2×2 ≤ 16 2×1 + 3×2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 

 

 Question 20  

  Consider the following minimization problem: Min z = x1 + 2×2 s.t. x1 + x2 ≥ 300 2×1 + x2 ≥ 400 2×1 + 5×2 ≤ 750 x1, x2 ≥ 0 Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

Multi Choice Problems

/in /by
Question 1 of 20
 5.0/ 5.0 Points
You have 332 feet of fencing to enclose a rectangular region. What is the maximum area?
A. 6889 square feet  
B. 6885 square feet  
C. 110,224 square feet  
D. 27,556 square feet  

Question 2 of 20
 0.0/ 5.0 Points
x varies inversely as y2, and x = 4 when y = 10. Find x when y = 2.
A. x = 16  
B. x = 5  
C. x = 80  
D. x = 100  

Question 3 of 20
 5.0/ 5.0 Points
Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function decreasing?
A. 10 through 25 and 40 through 45  
B. 10 through 25 and 40 through 50  
C. 0 through 10 and 25 through 40  
D. 10 through 50  

Question 4 of 20
 0.0/ 5.0 Points
x varies inversely as v, and x = 48 when v = 8. Find x when v = 64.
A. x = 6  
B. x = 64  
C. x = 8  
D. x = 48  

Question 5 of 20
 0.0/ 5.0 Points
The graph of a quadratic function is given. Determine the function’s equation.
A. j(x) = -x2 + 1  
B. f(x) = -x2 – 2x – 1  
C. h(x) = -x2 – 1  
D. g(x) = -x2 + 2x + 1  

Question 6 of 20
 5.0/ 5.0 Points
A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow.
A. 5 inches  
B. 4 inches  
C. 4.5 inches  
D. 5.5 inches  

Question 7 of 20
 0.0/ 5.0 Points
Find the indicated intercept(s) of the graph of the function.

x-intercepts of f(x) =

A. (-7, 0)  
B.  
C. (7, 0)  
D. none  

Question 8 of 20
 0.0/ 5.0 Points
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.

x2– 4x – 12 ≤ 0
A.
[6, ∞)		  
B.
(-∞, -2]		  
C.
(-∞, -2] [6, ∞)		  
D.
[-2, 6]		  

Question 9 of 20
 0.0/ 5.0 Points
Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x3 – 5x2– 9x – 2
A. {1, -2, -2 + , -2 – }  
B. {-1, -2, -2 + , -2 – }  
C. {-1, 3, -2 + , -2 – }  
D. {-1, 2, -2 + , -2 – }  

Question 10 of 20
 0.0/ 5.0 Points
Find the y-intercept for the graph of the quadratic function.

y + 4 = (x + 2)2
A. (0, 4)  
B. (0, 0)  
C. (4, 0)  
D. (0, -4)  

Question 11 of 20
 5.0/ 5.0 Points
Find the zeros of the polynomial function.

f(x) = x3 + 5x2– 4x – 20
A. x = -5, x = 4  
B. x = -2, x = 2  
C. x = -5, x = -2, x = 2  
D. x = 5, x = -2, x = 2  

Question 12 of 20
 0.0/ 5.0 Points
Use the Rational Zero Theorem to list all possible rational zeros for the given function.

f(x) = -2x3 + 4x2– 2x + 8
A. ± , ± , ± , ± 1, ± 2, ± 4, ± 8  
B. ± , ± 1, ± 2, ± 4, ± 8  
C. ± , ± , ± 1, ± 2, ± 4, ± 8  
D. ± , ± 1, ± 2, ± 4  

Question 13 of 20
 5.0/ 5.0 Points
While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 10 feet per second per second when the radius of the turn is 70 feet, find the acceleration the passengers feel when the radius of the turn is 140 feet.
A. 8 feet per second per second  
B. 6 feet per second per second  
C. 7 feet per second per second  
D. 5 feet per second per second  

Question 14 of 20
 0.0/ 5.0 Points
Find the vertical asymptotes, if any, of the graph of the rational function.

f(x) =

A. x = 1  
B. x = -1  
C. x = -1, x = 1  
D. no vertical asymptote  

Question 15 of 20
 0.0/ 5.0 Points
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. (2x + 1)(3x – 4) > 0
A.   
  
B.
 
C.
 
D.
 

Question 16 of 20
 0.0/ 5.0 Points
Find the vertical asymptotes, if any, of the graph of the rational function.

f(x) =

A. x = 4 and x = 4  
B. x = 4  
C. x = 0 and x = 4  
D. no vertical asymptote  

Question 17 of 20
 5.0/ 5.0 Points
If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 9 kilograms accelerates at a rate of per second per second by a force, find the rate of acceleration of an object with a mass of that is pulled by the same force.
A. 3 meters per second per second  
B. 27 meters per second per second  
C. 18 meters per second per second  
D. 24 meters per second per second  

Question 18 of 20
 0.0/ 5.0 Points
Add or subtract as indicated and write the result in standard form. 5i – (-5 – i)
A. -5 + 4i  
B. -5 – 6i  
C. 5 + 6i  
D. 5 – 4i  

Question 19 of 20
 0.0/ 5.0 Points
Find the range of the quadratic function.

f(x) = (x + 8)2– 7
A. [-7, ∞)  
B. (-∞, -8]  
C. [-8, ∞)  
D. (-∞, -7]  

Question 20 of 20
 5.0/ 5.0 Points
Determine whether the function is a polynomial function.

f(x) = – x2+ 3
A. No  
B. Yes  

 

statistics project 1

/in /by
Table 1:  Time (in Hours) Spent Each Week on a Resort Activity            
                         
Activity 1 2 3 4 5 6 7 8 9 10    
Archery 54.1 54.5 55.1 42.8 52.0 59.6 58.7 47.2 44.6 58.8    
Boating 49.8 64.7 58.8 60.2 58.5 60.0 69.7 61.7 57.0 69.5    
Canoeing 46.4 58.6 50.3 62.3 43.5 67.2 50.6 52.9 65.9 51.4    
Fishing 68.1 96.3 80.2 52.1 53.4 60.7 95.4 76.6 86.2 94.7    
Golfing 556.0 652.1 660.3 500.2 625.3 699.4 676.1 607.9 551.5 630.0    
Horseback Riding 72.8 83.5 67.7 83.9 51.8 56.3 69.0 74.8 85.3 66.8    
Jet Skiing 63.6 56.0 64.0 53.0 65.7 49.1 48.4 55.0 56.0 51.2    
Kayaking 60.0 66.9 61.1 88.5 87.3 87.9 99.6 86.2 50.8 90.9    
Sailing 61.7 65.1 53.1 47.9 41.0 42.1 42.8 58.1 67.4 49.1    
Tennis 57.1 44.4 46.2 43.5 46.8 55.3 66.9 50.1 64.3 60.4    
Tubing 44.2 46.3 57.5 58.9 61.3 43.2 59.2 54.8 45.3 43.3    
Water Skiing 55.1 49.2 52.2 64.2 49.5 61.1 45.5 43.7 61.8 53.7    
                         
Table 2:  Survey Responses
Guest First Favorite Activity Second Favorite Activity Number of Activities Tried Overall Rating of  Resort Activities Will Return in the Future?
1 Golfing Fishing 10 5 No
2 Horseback Riding Boating 9 4 Maybe
3 Kayaking Tubing 9 4 Maybe
4 Tennis Golfing 7 4 Yes
5 Golfing Sailing 5 3 Maybe
6 Fishing Horseback Riding 8 5 Yes
7 Horseback Riding Boating 12 5 Maybe
8 Kayaking Canoeing 4 3 No
9 Golfing Horseback Riding 5 2 Maybe
10 Fishing Golfing 11 4 No
11 Kayaking Tubing 5 3 No
12 Tennis Horseback Riding 12 3 Yes
13 Sailing Golfing 12 5 Maybe
14 Golfing Kayaking 2 3 Yes
15 Fishing Canoeing 10 5 Yes
16 Horseback Riding Fishing 11 5 Maybe
17 Horseback Riding Sailing 9 3 Yes
18 Canoeing Jet Skiing 5 4 No
19 Archery Kayaking 10 5 Yes
20 Sailing Golfing 8 4 Maybe
21 Tubing Kayaking 9 5 Maybe
22 Golfing Kayaking 7 5 No
23 Kayaking Tennis 8 4 Yes
24 Golfing Kayaking 7 5 Yes
25 Golfing Canoeing 7 4 No
26 Jet Skiing Golfing 10 3 Maybe
27 Golfing Kayaking 6 3 No
28 Golfing Fishing 7 3 Yes
29 Canoeing Fishing 9 5 Yes
30 Fishing Water Skiing 8 5 Yes
31 Fishing Boating 12 5 Yes
32 Kayaking Tennis 10 4 Maybe
33 Jet Skiing Tennis 8 4 No
34 Horseback Riding Fishing 12 4 Maybe
35 Boating Canoeing 9 4 Yes
36 Fishing Water Skiing 10 4 No
37 Golfing Jet Skiing 5 3 No
38 Canoeing Horseback Riding 11 4 Maybe
39 Kayaking Horseback Riding 7 1 No
40 Boating Golfing 8 4 Yes
41 Horseback Riding Fishing 7 5 Yes
42 Jet Skiing Kayaking 12 4 Yes
43 Canoeing Fishing 4 2 No
44 Kayaking Golfing 8 4 Yes
45 Kayaking Canoeing 5 2 No
46 Canoeing Water Skiing 10 3 Maybe
47 Water Skiing Boating 3 3 No
48 Golfing Sailing 12 5 Yes
49 Boating Tennis 8 3 No
50 Golfing Fishing 9 5 Yes
51 Golfing Archery 12 4 Maybe
52 Kayaking Golfing 4 3 Maybe
53 Fishing Canoeing 10 4 Maybe
54 Fishing Jet Skiing 4 3 Yes
55 Fishing Canoeing 3 4 No
56 Golfing Canoeing 11 4 Maybe
57 Golfing Kayaking 10 3 Maybe
58 Kayaking Tennis 11 5 Yes
59 Tennis Kayaking 10 5 Yes
60 Fishing Archery 2 2 No
61 Water Skiing Horseback Riding 10 4 Yes
62 Fishing Jet Skiing 10 4 Yes
63 Fishing Golfing 7 2 Maybe
64 Golfing Fishing 7 5 Yes
65 Golfing Archery 2 4 Yes
66 Canoeing Golfing 11 5 Yes
67 Archery Golfing 10 5 Yes
68 Kayaking Golfing 3 2 No
69 Kayaking Archery 9 5 Yes
70 Horseback Riding Golfing 4 5 No
71 Fishing Golfing 7 5 Maybe
72 Kayaking Horseback Riding 8 4 Yes
73 Archery Kayaking 12 4 Yes
74 Kayaking Canoeing 12 4 Maybe
75 Archery Sailing 9 4 Maybe
76 Kayaking Jet Skiing 6 3 Maybe
77 Horseback Riding Golfing 5 2 No
78 Golfing Kayaking 2 1 No
79 Golfing Fishing 10 3 Maybe
80 Golfing Archery 6 4 Maybe
Table 3:  Number of Resort Guests and the Number of Resort Activities Available
     
Year Number of Resort Activities Available (x) Number of Resort Guests (y)
2004 4 800
2005 4 850
2006 5 925
2007 6 950
2008 6 900
2009 9 1000
2010 11 1250
2011 12 1375

Here is the tables you will need to work with in excel but I need to jump on another computer to send all the information. Mine is messing up.

 
2015-02-02 19:24

 
2015-02-02 19:31

 

 

 Tis is the instructions for it.

 

 

 

 

• This project may be turned in via Oncourse Assignments or at my office (Hayes 255-R). If I am not there, place it under the door.

 

• Students can work individually or in groups. The maximum group size allowed is three (3).

 

• Students are to maintain academic honesty and professionalism while working on this project. If you elect to work on this project by yourself, then the work must be your own. If you elect to work on this project in a group then you can only work with your group members. There is to be no sharing of work among other groups or people outside of your group. Any use of someone else’s work outside of your group or another individual’s work will result in a zero for the project and possible other academic ramifications. If you have any questions regarding this please let me know.

 

• If working in groups, each group member must contribute to the project.

 

• If working in groups, please turn in only one (1) completed project file.

 

 

 

 

• If working in groups, please clearly list all group members.

 

 

 

• The work needs to be clear and well organized. Points will be deducted for work that is not clear or missing.

 

 

 

• Clearly label each part of the project.

• Note, you can use Excel, Word, or do the project by paper and pencil / pen. Work done by paper and pencil/pen can then be scanned if you are submitting the project via Oncourse Assignments. I will also take paper copies at my office.

 

• All the data for the project can be found in the Excel file: Project1_Data. There are three worksheets in this Excel file. See the case below for information regarding the data.

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

Liz has spent the summer interning as an assistant to the activities director at a beautiful resort. The resort property has two challenging 18 hole golf courses, numerous trails for horseback riding and hiking, and borders a large beautiful lake. The major resort activities include horseback riding, kayaking, canoeing, sailing, tubing, boating, jet skiing, water skiing, fishing, golfing, archery, and tennis.

 

 

 

There has been some talk lately about paring down the number of resort activities. Joan, the activities director, is wondering if there are too many activities for the guests. Perhaps, the resort should only concentrate on a few activities such as golf and leave other activities such as kayaking and horseback riding to local companies specializing in outdoor interests. Joan is concerned that guests are inundated with too many choices and feel as if they must try everything in order to get their money’s worth. In addition, the director is concerned about the costs of maintaining and the difficulty of scheduling all the different resort activities for the guests.

 

 

 

Liz has enjoyed her summer internship, especially working for Joan. She has gained some valuable work experience and would love to one day work as a manager at the resort once she finishes her undergraduate business degree. As her internship winds down, Liz wonders how she might be able to help Joan in her decision making regarding the resort activities.

By nature Liz is a numbers person. She enjoys collecting and analyzing data. Out of curiosity, Liz has been keeping track of the time spent (each week) on the major resort activities for the past ten weeks. Table 1 (see Excel file) shows the amount of time (in hours) spent each week by guests on a particular resort activity. For example, in Week 3 the total time spent by guests on tennis and kayaking was 46.2 hours and 61.1 respectively. The time spent per week is higher for golf since one typical round of golf usually takes four to five hours and resort guests usually play a few rounds per week. Liz decides to spend some time analyzing this collected data.

 

 

 

 

In addition, Liz decides to conduct a short survey for departing guests concerning their resort activities experience. Liz includes the following questions in her survey:

 

 

 

1) What was your first favorite activity?

 

3

 

 

 

 

 

2) What was your second favorite activity?

 

 

 

3) How many resort activities did you try during your stay?

 

 

 

4) On a scale from 1 to 5 (where 5 is the highest, 1 is the lowest), please rate the overall quality of the resort activities.

 

 

 

5) Do you plan on returning to the resort in the future?

Liz ends up surveying 80 departing guests. Table 2 (see Excel file) contains the responses for the 80 guests who took her survey. For example, Guest 6 indicated that fishing and horseback riding were the guest’s first and second favorite resort activities. Guest 6 tried eight activities during his/her stay, gave the resort a 5 for overall activity quality, and does plan on returning to the resort in the future.

 

Finally, Liz is curious to see if there is a relationship between the number of activities available and the number of guests coming to the resort each year. She does some digging and is able to retrieve the number of major activities available and the number of guests coming to the resort for the years 2004 to 2011. The resort opened to guests in May 2001. Table 3 (see Excel file) shows the number of major resort activities available and the number of guests that stayed at the resort for the years 2004 to 2011. For example, in 2009 there were 1000 resort guests and nine major activities available.

 

 

 

 

Liz decides to spend the final week of her summer internship organizing and analyzing all this collected data. Before departing she will provide Joan with a report of her findings and analysis. Liz is hoping that the report will be helpful to Joan as she makes decisions concerning future activities at the resort. Liz plans on including tables, graphs, numerical measures, observations, and recommendations in the report.

 

Project Requirements

 

 

 

The following needs to be included in one’s report:

 

 

 

 

 

 

 

1) Create frequency and relative frequency distributions for the first and second favorite guest activities. One will find this data in the Table 2 worksheet of the Excel file.

• Total points possible for this section: 10 points

 

• The frequency and relative frequency distributions for the first favorite activity are worth 5 points.

 

 

 

 

• The frequency and relative frequency distributions for the second favorite activity are worth 5 points.

 

 

 

• Rubric for the distributions:

o 4 to 5 points: Done correctly or there is a minor error

 

 

 

 

 

 

4

 

 

 

 

o 2 to 3 points: Has made a decent attempt; however, there are errors.

 

o 0 to 1 points: Has not attempted or has not made a decent attempt.

 

 

 

 

2) Create bar graphs that show the frequencies for the first and second favorite resort activities. The bar graphs should include titles for the horizontal axis and vertical axis and data labels. One will find this data in the Table 2 worksheet of the Excel file.

• Total points possible for this section: 10 points

 

• Each bar graph is worth 5 points.

 

 

 

 

• Rubric for each bar graph:

o 4 to 5 points: Done correctly or there is a minor error. Titles for the vertical axis and horizontal axis and labels showing the data values are present in the bar graphs. The bar graph has gaps between categories.

 

o 2 to 3 points: Has made a decent attempt; however, there are errors. Missing titles and/or labels. No gaps between categories.

 

o 0 to 1 points: Has not attempted or has not made a decent attempt.

 

 

 

 

3) Create a pie chart that shows the percentages of the survey responses for the question “Do you plan on returning to the resort in the future?” One will find the responses in the Table 2 worksheet of the Excel file. Note, there are three possible answers: Yes, No, and Maybe. Be sure to note the categories and percentages on the pie chart and include a legend.

• Total points possible for this section: 5 points

 

• Rubric:

 

o 4 to 5 points: Done correctly or there is a minor error. Pie chart has labels showing the categories and percentages and a legend.

 

o 2 to 3 points: Has made a decent attempt; however, there are errors. Missing categories, percentages, and/or legend.

 

o 0 to 1 points: Has not attempted or has not made a decent attempt.

 

 

 

 

4) Create a histogram for the number of resort activities tried by the guests. This data can be found in the Table 2 worksheet of the Excel file. Use the following classes for the histogram.

 

 

 

1 to 2

 

 

 

3 to 4

 

 

 

5 to 6

 

 

 

7 to 8

 

 

 

9 to 10

 

 

 

11 to 12

 

5

 

 

 

 

• Total points possible for this section: 5 points

 

• Rubric:

 

o 4 to 5 points: Done correctly or there is a minor error. The histogram has titles for the vertical axis and horizontal axis and labels showing the data values. Histogram contains no gaps.

 

o 2 to 3 points: Has made a decent attempt; however, there are errors. Missing titles and/or labels. Histogram has gaps.

 

o 0 to 1 points: Has not attempted or has not made a decent attempt.

 

 

 

 

5) Create a table that shows the different resort activity ratings and the number of guests that selected each of these ratings. Then calculate the weighted mean (average) of the ratings. The data can be found in the Table 2 worksheet of the Excel file.

• Total points possible for this section: 7 points

 

• Rubric: o 6 to 7 points: Done correctly or there is a minor error

 

o 3 to 5 points: Has made a decent attempt; however, there are errors or missing some information.

 

o 0 to 2 points: Has not attempted or has not made a decent attempt.

 

 

 

 

　

 

 

 

6) Calculate the following numerical measures: mean, median, sample variance, sample standard deviation, range, and coefficient of variation for each resort activity. The data (time spent each week on a resort activity) can be found in the Table 1 worksheet of the Excel file. In a table list each activity and the numerical measures (e.g. mean, median) calculated for each activity.

• Total points possible for this section: 12 points

 

• Rubric: o 9 to 12 points: Done correctly or there are a few minor errors.

 

o 5 to 8 points: Has made a decent attempt; however, there are errors or missing some information.

 

o 0 to 4 points: Has not attempted or has not made a decent attempt. Many errors.

 

 

 

 

　

 

 

 

7) Create a scatter diagram to see if there is a relationship between the number of resort activities available and the number of resort guests. The data can be found in the Table 3 worksheet of the Excel file.

• Total points possible for this section: 5 points

 

 

 

 

 

 

6

 

 

 

 

• Rubric:

 

o 4 to 5 points: Done correctly or there is a minor error. The scatter diagram includes titles for the vertical axis and horizontal axis.

 

o 2 to 3 points: Has made a decent attempt; however, there are errors.

 

o 0 to 1 points: Has not attempted or has not made a decent attempt.

 

 

 

 

8) Calculate the sample covariance and sample correlation coefficient to see whether there is a relationship between the number of resort activities available and the number of resort guests. The data can be found in the Table 3 worksheet of the Excel file.

• Total points possible for this section: 6 points

 

• Rubric: o 5 to 6 points: Done correctly or there is a minor error

 

o 3 to 4 points: Has made a decent attempt; however, there are some errors.

 

o0 to 2 points: Has not attempted or has not made a decent attempt. There are errors.

 

 

 

 

　

9) Finally, your report needs to include a write-up that notes observations and recommendations. These observations and recommendations should be based on and reference your tables, graphs, and calculations. The write-up should be a minimum of three paragraphs (each paragraph should include at least three complete sentences) and refer to your tables, graphs, and calculations. Use correct grammar and spelling in your write-up.

 

 

 

 

At least the following needs to be included in your write-up. Be sure your statements refer to your graphs, tables, and calculations.

 

 

 

1) Discuss what are the most popular and least popular resort activities.

 

 

 

2) Discuss the number of resort activities tried by the guests.

 

 

 

3) Discuss the resort activity ratings.

 

 

 

4) Discuss whether guests will return.

 

 

 

5) Discuss whether there is a relationship between the number of resort activities available and the number of resort guests based on your scatter diagram and covariance and correlation calculation results.

 

 

 

6) What recommendations would you make to Joan, the activities director, regarding future resort activities?

 

 

 

You may also include other observations and recommendations based on the results of your tables, graphs, and numerical measures.

 

7

 

 

 

 

• Total points possible for this section: 15 points

 

• Rubric: o 12 to 15 points: The write-up is well written (few or no grammar and spelling issues), is at least three paragraphs in length, and addresses most or all the requirements listed above. Your statements are correct and are backed up by references to the tables, graphs, and calculations. Minor mistakes.

 

 

 

 

　

o 7 to 11 points: A decent attempt at the write-up. However, there may be some grammar, spelling, and/or length issues. Also, it is possible that not all points are addressed in the report or one’s statements are not backed up by references to the tables, graphs, and calculations.

 

o 0 to 6 points: Has not attempted or has not made a decent attempt at the write-up. There are serious grammar, spelling, and/or length issues. The write-up does not include all the requirements and / or does not sufficiently reference the tables, graphs, and calculations.

 

SHOW ALL WORK!!

 

Stats Help

/in /by

Computer Assignment # 3 (Illustration of Central Limit Theorem)

 

 

Instructions

 

 

As you do this exercise, remember that neatness counts.  If you type something into a cell, you mayneed to resize the cell to make it readable (by me).  Complete the instructions as written.  If I expect you to answer a question on the spreadsheet, I will tell you in which cell to write the answer.  Remember to save your work often. 

 

 

What are we trying to do?

 

The intent of this exercise is to observe firsthand the impact of the Central Limit Theorem: under repeated sampling, the distribution of a sample mean () has a normal distribution.  We will do this by sampling n = 36 values from a continuous uniform random variable, X, on [0, 10] and observing the characteristics of .

 

(1)   Open a new file in Excel.  Rename the first worksheet of that file Population.  Fill in your worksheet as shown below.

 

 

figure1.jpg

 

 

 

Next use the following formulas for uniform distributions to fill in B6:B7.

 

 

Use an appropriate command to find the standard deviation of x in B8.

 

Next fill in the values of the mean, variance, and standard deviation of  in C6:C8 using formulas involving B6:B8and the facts

 

E[] = E[X]

 

Var() = Var(X)/n

 

 

*****Save your work.*****  (Save using your “last name_Comp3” as the file name)

 

 

At this point, you know the mean, variance, and standard deviation of two populations: (1) the population from which we will be sampling, which has a uniform distribution on [0,10]; and (2) the population of , which should have an approximate normal distribution according to the Central Limit Theorem.

 

(2)   Select a new worksheet and rename it Samples.  We will use the first row for labels. In A1 write “Samples”.  In B1:AK1 write the labels X1, X2, … X36.  These values represent the 1st, 2nd, …,36th values in our sample.  In AL1 write X-Bar.  Underline the labels (by right-clicking on the cells and choosing Format Cells – Border to outline only the bottom of the cells).

(3)   Returning to A2, we type “1” to indicate this is our first sample.  So how do we perform our sample?

 

Rand

 

 

As shown above and as I illustrated in class, Excel has a function entitled RAND() which will automatically generate a value uniformly distributed on [0,1].  This function does not have arguments, but you do have to use opened and closed parentheses after its name.  To get a value uniformly distributed on [0,10], you simply have to compute

 

=10*rand()

 

If you type this in B2, you can copy it to cells C2:AK2 to get our first sample of size 36.  In AL2, compute the average of these 36 values.  Be sure not to include the number in A2. 

 

All of your sample values as well as the sample mean should be between 0 and 10.  Hit F9 (recalculate) a few times to observe different samples being selected.

 

*****Save your work.*****

 

(Note:  We are about to create 1000 samples like the one above and build some frequency distributions based on our results.  The function RAND() will recalculate every time something new is added to the spreadsheet.  Excel does this quickly, and it is not a problem to your work.  Some people find this feature of Excel unnerving.  You may choose to stop the automatic recalculation if you like, but you do not need to disable it if this doesn’t bother you.If you would like to stop the automatic recalculation, choose File and then Options (second from the bottom of this menu)  Now select the second option called Formulas.

 

Recalculate in EXCEL 2007

 

 

Select the Manual button.  You can use the same procedure to turn automatic recalculation on later.  Important point—since you turned off the automatic recalculation, you will not see the system respond as you are accustomed.  You can and should hit F9 to make the system recalculate to check your calculations as you go through this exercise.)

 

(4)   Number the samples 2-1000 in A3:A1001.  One way to do this is to type “2” in A3, select A2:A3, and copy. 

(5)   Copy the cells in B2:AL2 to rows 3:1001.  If you turned off the automatic recalculation, the samples look exactly the same.  Press F9.

 

The 1000 values in AL2:AL1001 are 1000 sample means computed by taking samples of size 36 from a population uniformly distributed on [0,10].

 

*****Save your work.*****

 

(6)   Next we want to look at the values of the sample means and verify that they seem to be coming from a normal distribution with a mean of 5.0 and a standard deviation of 0.481.  In AN1 type “X-bar Avg”.  In AN2 type “X-bar Stdev”.  In AO1, compute the mean for the 1000 X-bar values.  In AO2, compute the standard deviation of the 1000 X-bar values found in AL2:1001.  Do your values look like what we expect?

(7)   Now we will construct a frequency distribution of the X-bar values.  Go back to the Population worksheet and inE1 type “No. ofStdDev”.  In E2:15 type the numbers: -3, -2.5, -2, -1.5, -1, -0.5, 0, .5, 1, 1.5, 2, 2.5, 3, 10.4.  In F1 type the label “Bins”.  In F2 perform the calculation

 

=$C$6+E2*$C$8

 

Copy this calculation to F3:F15.

 

In G2, describe what the number in F2 means, using your knowledge of what the values in C6 and C8 are.Notice that the last value, 10.4, was chosen so that the last bin would contain the largest possible sample means, which cannot exceed 10.

 

Select E1:F15 and select copy.  Return to the Samples worksheet and go to cell AQ1.  Under Paste, select Paste Special and select values as shown below.

 

Paste%20special

 

Reduce the number of decimal places used under “Bins” to 2.

*****Save your work.*****

 

 

(8)   In AS1 type “Cumulative”.  In AS2 type

 

=FREQUENCY($AL$2:$AL$1001,AR2)

 

Recall from our first laptop exercise that the frequency function takes an array as the first argument and returns the count of all values smaller than the second argument.  Copy this function to AS3:AS15.

 

(9)   In AT1 type “Frequency”.  Use the cumulative frequencies in column AS to create the bin frequencies in AT2:AT15.

 

(10)  In AU1 type “Normal Prob”.  Use the function normsdist and the number of standard deviations in column AQ to construct the cumulative standard normal distribution in AU2:AU15.  For example, AU2 would appear as

 

=NORMSDIST(AQ2)

 

Copy this calculation to AU3:AU15.

 

(11)  In AV1 type “Expected Cumulative”.  Multiply each of the values in column AU by 1000.  For example, AV2 would appear as

 

=1000*AU2

 

The values in column AV represent the number of times in our production of 1000 sample means we expect to see a sample mean fall below the bin value in column ARif the sample means are normally distributed.

 

(12)  In AW1 type “Expected Frequency”.  Use the cumulative frequencies in column AV to compute the expected frequencies for each bin.  (Note: this computation is exactly the same computation you did in constructing column AT.)

 

 

*****Save your work.*****

 

 

(13)  Graph the frequencies in column AT and the expected frequencies in column AW using a column chart.  The x-axis should be labeled with values corresponding to the number of standard deviations away from the mean (the values found in column AQ).  To format the x-axis in this manner, click one of the x-axis values so the entire set of values is selected.  Then right click and choose “select data.”  A box will appear which asks you to select the data source.  On the right-hand side, you will see an option for “Horizontal (Category) Axis Labels.”Under this, click “Edit” and then select the corresponding data in column AQ.   Be sure to label the axes on your graph and give the chart an appropriate title as well. 

 

 

*****Save your work.*****

 

 

 

Using your graph, compare the frequencies with the expected frequencies.  Now you can hit F9 to resample.  Do this several times.  Visually, do the values of  appear to be coming from a normal distribution?

statistics midterm

/in /by

Homework #6

Use the following scenario to answer the next 3 questions.  Plastic bags used for packaging produce are manufactured so that the breaking strength of the bag is normally distributed with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch.   A sample of 25 bags is selected. So we have that the breaking strength of the bags is normal with µ=5 lbs/in2 and σ = 1.5 lbs/in2.   Also, n = 25.

1)         What is the probability that the average breaking strength is between 5 and 5.5 pounds per square inch?

 

 

 

 

2)         What is the probability that the average breaking strength is between 4.2 and 4.5 pounds per square inch?

 

 

 

 

 

3)         What is the probability that the average breaking strength is less than 4.6 pounds per square inch?

 

 

 

 

 

 

 

 

 

 

 

 

 

Use the following scenario to answer the next 3 questions.  Historically, 93% of the deliveries of an overnight mail service arrive before 10:30 the following morning.   Random samples of 500 deliveries are selected.  So we have a “historic” (read: population) proportion of p = .93.

Also, n = 500.

 

4)         What proportion of the samples will have between 93% and 95% of the deliveries arriving before 10:30 the following morning?

 

 

 

 

5)         What proportion of the samples will have more than 95% of the deliveries arriving before 10:30 the following morning?

 

 

 

 

 

6)         What is the proportion of the samples will have less than 90% of the deliveries arriving before 10:30 the following morning?