Mathematics - College School Essays

statistics -6

October 13, 2023/in Mathematics /by elias

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?

MAT 540 Final Exam

October 13, 2023/in Mathematics /by elias

MAT 540 Week 11 Final Exam

1. Which of the following could be a linear programming objective function?

2. Which of the following could not be a linear programming problem constraint?

3. Types of integer programming models are _____________

4. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. 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. If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of

5. The reduced cost (shadow price) for a positive decision variable is 0

TRUE/FALSE

6. Decision variables

7. A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in the

8. Decision models are mathematical symbols representing levels of activity.

TRUE/FALSE

9. The integer programming model for a transportation problem has constraints for supply at each source and demand at each destination.

TRUE/FALSE

10. In a transportation problem, items are allocated from sources to destinations

11. 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 ___.

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

13. In a linear programming problem, a valid objective function can be represented as

14. 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

15. Constraints representing fractional relationships such as the production quantity of product 1 must be at least twice as much as the production quantity of products 2, 3 and 4 combined cannot be input into computer software packages because the left side of the inequality does not consist of consists of pure numbers.

TRUE/FALSE

16. In a balanced transportation model where supply equals demand

17. The objective function is a linear relationship reflecting the objective of an operation.

TRUE/FALSE

18. 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?

19. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

TRUE/FALSE

20. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from

3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the

21. In a total integer model, all decision variables have integer solution values.

TRUE/FALSE

23. Linear programming is a model consisting of linear relationships representing a firm’s decisions given an objective and resource constraints.

TRUE/FALSE

24. When using linear programming model to solve the “diet” problem, the objective is generally to maximize profit.

TRUE/FALSE

25. In a balanced transportation model where supply equals demand, all constraints are equalities.

TRUE/FALSE

26. In a transportation problem, items are allocated from sources to destinations at a minimum cost.

TRUE/FALSE

27. Mallory 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. Which of the following is not a feasible purchase combination?

28. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

TRUE/FALSE

29. In a 0 – 1 integer model, the solution values of the decision variables are 0 or 1.

TRUE/FALSE

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

TRUE/FALSE

31. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints’ prices.

TRUE/FALSE

32. The transportation method assumes that

33. A constraint is a linear relationship representing a restriction on decision making.

TRUE/FALSE

34. When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell.

TRUE/FALSE

35. The linear programming model for a transportation problem has constraints for supply at each ________ and _________ at each destination.

36. The 3 types of integer programming models are total, 0 – 1, and mixed.

TRUE/FALSE

37. In using rounding of a linear programming model to obtain an integer solution, the solution is

38. If we use Excel to solve a linear programming problem instead of QM for Windows,

then the data input requirements are likely to be much less tedious and time consuming.

TRUE/FALSE

39. In a _______ integer model, some solution values for decision variables are integer and others can be non-integer.

40. Which of the following is not an integer linear programming problem?

need right know

October 13, 2023/in Mathematics /by elias

What is the term called for a proper APA citation where the 2nd and subsequent lines in a citation are inwardly spaced one tab length?

2 what part of a properly APA formatted paper summarizes the paper in about 250 words

3 What does it mean when a journal article is peer reviewed?

4 Which of the following is not important in evaluating the quality of research?

5 Which of the following cases is plagiarism?

6. Which of the following is not accomplished in qualitative research?

7. What kind of research is meant to see humans in their natural habitats?

8. Which of the following is true?

9 You want to do research on the impact of a new drug on depression. What is the independent variable?

10 You want to do research on the impact of a new drug on depression. What is the dependent variable?

C499 need answer right away

NEW POST MAT540

October 13, 2023/in Mathematics /by elias

MAT540 Homework Week 8 Page 1 of 4

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:

page1image6864

Ore	Metal (%)				Impurities (%)	Cost/Ton
Ore	A	B	C	D	Impurities (%)	Cost/Ton
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.

2. 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.

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

Program	Votes/ Dollar
Job training	0.02
Parks	0.09
Sanitation	0.06
Mobile library	0.04

MAT540 Homework Week 8 Page 2 of 4

 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.

Formulate a linear programming model for this problem.
Solve the model by using the computer.

3. 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.

MAT540 Homework Week 8 Page 3 of 4

Solve the model by using the computer
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?

4. 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:

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.

Formulate a linear programming model for this problem.
Solve this model by using the computer.

5. 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

Mine	% Ash	% Sulfur
1	9	6
2	5	4
3	4	3

MAT540 Homework Week 8 Page 4 of 4

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.

Formulate a linear programming model for this problem.
Solve the model by using the computer
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?

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

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.

Formulate a linear programming model for this problem.
Solve the model by using the computer
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?

free answer

October 13, 2023/in Mathematics /by elias

SAMPLING

NAME:

INSTITUTION:

DATE:

            From the above analysis, the several conclusion can be reached and also several observation. It is clear that after sampling we were able to get the entire time. After this, we were able to get the quintile range, median. This includes the upper and the lower quintile range that is Q1 and Q3. With this arrangement, we can be able to arrange the entire field and how the game is organized where most of the players are concentrated at the center of the field. This is turn to be one of the importance of sampling.
            The data was able to give us a precise arrangement of how the field will look like. Sampling is used to make a code that will be employed in a computer or a phone as a football game. Without sampling, it can de hand to get those games operate. The sampling helps us to get the most relevant summary of the entire data. The minimum and the maximum value that turn to be 175 and 300 respectively, the lower quintile and the upper quintile that was 196.25 and 238.75 respectively. We were also able to get the median that was 217.50.
            When a box-whisker of the samples was plotted, it turns to be a perfect shape of the football field is. The box and whisker plot deals with maximum and minimum values, shows the lower and the upper quartiles and is also based on the median. The sampling is one of the most important aspects of probability and statistic. It makes information and data to have to mean. It helps to come up with meaningful information.
            We use excel to calculate a sample mean that was 220.6 pounds and the sample standard deviation was 33.84 pounds. The sample saves us the struggle of getting the entire population mean. It saves our time, and it is the best way to estimate the population mean and standard deviation of the data. The actual population means and the standard deviation were calculated as 214.6 pounds and 42.2 respectively. This indicates that the sample of statistic fairly represent the whole population hence can be used to make conclusions on behalf of the entire population.
            The sample mean and the standard deviation were used to come up with the Empirical Rule graph. The Empirical Rule graph helps to get the skewness of the data alkalized. The rule is also applied in the distribution for normality test. The size of the deviations is computed in the form of standard deviation and compared to the expected frequency. In our case, we had a normal skewed graph. This means that the data follow the empirical rule and that the data can be used for further analysis.
            In conclusion, it is found that data sampling is imperative in coming up with a varied determination and data analysis. We realized that in most cases a sample of data usually represents the entire population. It is important to put in mind that when taking samples we must be very careful to take only the correct data from the entire population. This helps not to transfer errors from the primary data to analysis. The sample if well corrected in most cases it represent the population. It is important to put in mind that once a sample one end up getting the wrong analyzed data that read to the bad conclusion.

MAT 540 Week 8 Assignment 1 Linear Programming Case Study

October 13, 2023/in Mathematics /by elias

Click the link above to submit your assignment.

Students, please view the “Submit a Clickable Rubric Assignment” in the Student Center.

Instructors, training on how to grade is within the Instructor Center.

Assignment 1. Linear Programming Case Study

Your instructor will assign a linear programming project for this assignment according to the following specifications.

It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.

You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.

Writeup.

Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.

Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.

Excel.

As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.

Click here to view the grading rubric for this assignment.

Computer abuse by employees is an ongoing worry to businesses. A study revealed the data shown below. At α = .02, is the frequency of disciplinary action independent of the abuser’s level of privilege? Computer Abuse I

October 13, 2023/in Mathematics /by elias

1.
award:

10.00 points
Computer abuse by employees is an ongoing worry to businesses. A study revealed the data shown below.
At α = .02, is the frequency of disciplinary action independent of the abuser’s level of privilege?
Computer Abuse Incidents Cross-Tabulated by Privilege and Punishment
Level of Privilege
Disciplined
Not Disciplined
Row Total
Low
20
2
22
Medium
25
10
35
High
38
12
50

Col Total
83
24
107

Click here for the Excel Data File

Calculate the Chi-square test statistic, degrees of freedom and the p-value. (Round your test statistic
value to 2 decimal places and the p-value to 4 decimal places.)

Test statistic
d.f.
p-value

(a) The hypothesis for the given issue is H0: Privilege Level and Disciplinary Action are independent.

No

Yes
(c) Find the critical value for Chi-Square. Refer to the chi-square table. (Round your answers to 3 decimal
places.)
Critical value

(d) We can reject the null hypothesis and find dependence. Is the statement true or false?

TRUE
FALSE
Worksheet

Learning Objective: 15-01 Recognize a
contingency table.

Learning Objective: 15-03 Perform a chi-square
test for independence on a contingency table.

Difficulty: 2-Medium

Learning Objective: 15-02 Find degrees of
freedom and use the chi-square table of critical
values.

Learning Objective: 15-06 Use computer
software to perform a chi-square GOF test for
normality.

[The following information applies to the questions displayed below.]

At a local supermarket receiving dock, the number of truck arrivals per day is recorded for 100 days.

Arrivals per Day at a Loading Dock

0
1
2
Frequency
8
24
25

Number of Arrivals
3
21

4
8

5
7

6
6

7
1

Total
100

Click here for the Excel Data File

2.

award:

10.00 points
(a) Estimate the mean from the sample. (Round your answer to 2 decimal places.)
Sample mean
Worksheet

Difficulty: 3-Hard

Learning Objective: 15-05 Explain the GOF test
for a Poisson distribution.

3.

award:

10.00 points

(b-1) Carry out the chi-square test, combining end categories as needed to ensure that all expected
frequencies are at least five. (Perform a Poisson Goodness of Fit test for alpha = .01, combining
the last three categories into a single category for 5 or more. Do not round your intermediate
calculations. Round your answers to 4 decimal places.)

Chi-square
d.f.
p-value

Worksheet

Difficulty: 3-Hard

Learning Objective: 15-05 Explain the GOF test
for a Poisson distribution.

4.

award:

10.00 points
(b-2) Truck arrivals per day follow a Poisson process.
False
True
Multiple Choice

Difficulty: 3-Hard

Learning Objective: 15-05 Explain the GOF test
for a Poisson distribution.

MAT 540 Week 11 Final Exam

October 13, 2023/in Mathematics /by elias

1. Which of the following could be a linear programming objective function?

2. Which of the following could not be a linear programming problem constraint?

3. Types of integer programming models are _____________

4. The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. 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. If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of

5. The reduced cost (shadow price) for a positive decision variable is 0

TRUE/FALSE

6. Decision variables

7. A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in the

8. Decision models are mathematical symbols representing levels of activity.

TRUE/FALSE

9. The integer programming model for a transportation problem has constraints for supply at each source and demand at each destination.

TRUE/FALSE

10. In a transportation problem, items are allocated from sources to destinations

11. 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 ___.

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

13. In a linear programming problem, a valid objective function can be represented as

14. 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

15. Constraints representing fractional relationships such as the production quantity of product 1 must be at least twice as much as the production quantity of products 2, 3 and 4 combined cannot be input into computer software packages because the left side of the inequality does not consist of consists of pure numbers.

TRUE/FALSE

16. In a balanced transportation model where supply equals demand

17. The objective function is a linear relationship reflecting the objective of an operation.

TRUE/FALSE

18. 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?

19. The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

TRUE/FALSE

20. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from

3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the

21. In a total integer model, all decision variables have integer solution values.

TRUE/FALSE

23. Linear programming is a model consisting of linear relationships representing a firm’s decisions given an objective and resource constraints.

TRUE/FALSE

24. When using linear programming model to solve the “diet” problem, the objective is generally to maximize profit.

TRUE/FALSE

25. In a balanced transportation model where supply equals demand, all constraints are equalities.

TRUE/FALSE

26. In a transportation problem, items are allocated from sources to destinations at a minimum cost.

TRUE/FALSE

27. Mallory 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. Which of the following is not a feasible purchase combination?

28. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

TRUE/FALSE

29. In a 0 – 1 integer model, the solution values of the decision variables are 0 or 1.

TRUE/FALSE

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

TRUE/FALSE

31. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints’ prices.

TRUE/FALSE

32. The transportation method assumes that

33. A constraint is a linear relationship representing a restriction on decision making.

TRUE/FALSE

34. When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell.

TRUE/FALSE

35. The linear programming model for a transportation problem has constraints for supply at each ________ and _________ at each destination.

36. The 3 types of integer programming models are total, 0 – 1, and mixed.

TRUE/FALSE

37. In using rounding of a linear programming model to obtain an integer solution, the solution is

38. If we use Excel to solve a linear programming problem instead of QM for Windows,

then the data input requirements are likely to be much less tedious and time consuming.

TRUE/FALSE

39. In a _______ integer model, some solution values for decision variables are integer and others can be non-integer.

40. Which of the following is not an integer linear programming problem?

week 4 review

October 13, 2023/in Mathematics /by elias

1.

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

2.

Consider the linear programming problem.

Sketch the feasible set for the linear programming problem.

3.

Maximize

P= 10x + 12y

subject to

4.

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

5.

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

6.

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

7.

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

8.

Solve the linear system of equations

Unique solution:

Infinitely many solutions:

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.

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

11.

Solve the linear system of equations

Unique solution:

Infinitely many solutions:

12.

Solve the linear programming problem by the simplex method.

13.

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

14.

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

15.

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 +

16.

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

17.

Indicate whether the matrix is in row-reduced form.

18.

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.

19.

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

20.

Consider the linear programming problem.

Sketch the feasible set for the linear programming problem.

21.

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.

22.

Solve the linear system of equations

Unique solution:

Infinitely many solutions:

23.

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

24.

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

(2, 2) and (8, 5)

25.

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

infinitely many solutions

STAT 200 FALL 2014

October 13, 2023/in Mathematics /by elias

1. Determine whether the given value is a statistic or parameter. (4 pts)

(a) In a STAT 200 student survey, 20% of the respondents said that they had to take time off from work to study for the course.

(b) The average lifetime of all street lights in UMUC Academic Center is 20,000 hours.

2. True of False. (8 pts)

(a) Mean is a better measure of center than median because mean is not affected by extreme values from a data set.

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

(c) It is possible that a data set does not have a mode.

(d) P(AandA) 1, whereAis the complement ofA.

Refer to the following frequency distribution for Questions 3, 4, 5, and 6. 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
	Checkout Time (in minutes)		Frequency
	1.0 – 1.9		6
	2.0 – 2.9		5
	3.0 – 3.9		4
	4.0 – 4.9		3
	5.0 – 5.9		2

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 3 of 6

3.	What percentage of the checkout times was at least 4 minutes?	(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)

6. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase,

decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)

Refer to the following data to answer questions 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:

1 13 15 18 20

7. Find the standard deviation. (Round the answer to two decimal places) (10 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 without replacement from a 52-card deck. Let event A be the first card is a heart, and event B be the second card is a heart.

9. What is the probability that the first card is a heart and the second card is also a heart?

(Express the answer in simplest fraction form) (8 pts)

10. What is the probability that the second card is a heart, given that the first card is a heart?

	(Express the answer in simplest fraction form)	(8 pts)
11.	Are A and B independent? Why or why not?	(2 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 1500 juniors in a college. Among the 1500 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 in neither of the two courses?

(10 pts) 13. What is the probability that a randomly selected junior takes only one course? (10 pts)

Refer to the following information for Questions 14, and 15. Show all work. Just the answer, without supporting work, will receive no credit.

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 4 of 6

UMUC STAT Club must appoint a president, a vice president, and a treasurer. It must also select three members for the STAT Olympics team. There are 10 qualified candidates, and officers can also be on the STAT Olympics team.

14.	How many different ways can the officers be appointed?	(10 pts)
15.	How many different ways can the STAT Olympics team be selected?	(10 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	5
	P(x)	0.1	0.1	0.4	0.1	0.3

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 made random guesses at 5 true-or-false questions in a STAT 200 pop quiz. Let random number X be the number of correct answers Mimi got. As we know, the distribution of X is a binomial probability distribution. Please answer the following questions:

18. What is the number of trials (n), probability of successes (p) and probability of failures (q),

	respectively?		(5 pts)
19.	Find the probability that she got at least 3 correct answers	.	(10 pts)

20. Find the mean and standard deviation for the probability distribution. (Round the answer to two

decimal places) (10 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 between 6 and 15 feet tall?

		(10 pts)
22.	Find the 80th percentile of the dogwood tree height distribution.	(5 pts)

23. If a random sample of 144 dogwood trees is selected, what is the standard deviation of the sample

mean? (5 pts)

24. A random sample of 100 GMAT scores has a mean of 500. Assume that GMAT scoreshave a population standard deviation of 120. Construct a 95% confidence interval estimate of the

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 5 of 6

mean GMAT scores. 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.

H0: 750

H1: 750

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

(b) Determine the critical value. 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

H 0: p 0.5 H1: p0.5

In a random sample of 225 subjects, the sample proportion is found to be pˆ 0.55 .

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

(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 H0 at the0.01 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	10
2	18	14
3	11	9
4	16	12
5	15	12

STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL1 Page 6 of 6

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3?

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 by more than 3? Justify your conclusion. (25 pts)

Refer to the following data for Questions 28 and 29.

x	0	-1	3	2	5
y	3	-2	3	6	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. (10 pts)

30.	The UMUC Bookstore sells three different types of coffee mugs. The manager reported
	that the three types are purchased in proportions: 50%, 30%, and 20%, respectively.
	Suppose that a sample of 100 purchases yields observed counts 46, 28, and 26 for types
	1, 2, and 3, respectively.

			Type	1	2	3
			Number	46	28	26
	Assume we want to use a 0.10 significance level to test the claim that the reported
	proportions are correct.
	(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 reported proportions are
		correct? Justify your answer.

statistics -6

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STAT 200 FALL 2014

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