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Maths assignment

Page | 1 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Unit Code and Title: SBM3103 Mathematics and Statistics Assessment Overview Assessment Task Weighting Due Length ULO Assessment 1: Quiz In this assessment task student will sit for online quiz in week 3. This is an individual assignment. 10% Week 3 30 minutes [ULO1] Assessment 2: Case Study In this assessment task student will analyse data collected from a business case. This is an individual assignment. 20% Week 7 1000 words [ULO1], [ULO2], [ULO3], [ULO4] Assessment 3: Log/Workbook This assessment task is a weekly recording of the inside gained through a series of tutorial exercises. This is an individual task. Please find on Canvas for detailed description. 30% Weekly (Week 1 to Week 10) 15 hours tutorial work [ULO1], [ULO2], [ULO3], [ULO4] Assessment 4: Statistical Data Analysis In this assessment task students will perform statistical data analysis based on a data set provided. The data can be downloaded from Canvas under the Assessment 4 Task. This assessment task is an individual task. 40% Week 12 2000 Words [ULO1], [ULO2], [ULO3], [ULO4] Assessment Details Page | 2 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Assessment 1: Quiz Due date: Week 3 Group/individual: Individual (In class during tutorial session) Word count / Time provided: 30 minutes Weighting: 10% Unit Learning Outcomes: [ULO1] Assessment Details: Quiz questions will be based on the materials covered in lectures and tutorials as well as those assigned in these sessions. Quiz questions will be similar to tutorial questions and will require use of a calculator. Multiple choice, short answer questions and quantitative problems may be included in the quiz. Marking Information: The quiz will be marked out of 100 and will be weighted 10% of the total unit marks. Page | 3 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Assessment 2: Case Study Due date: Week 7 Group/individual: Individual Word count / Time provided: 1000 Words Weighting: 20% Unit Learning Outcomes: [ULO1], [ULO2], [ULO3], [ULO4] Assessment Details: The SBM3103 assessment task 2 is worth of 20% of the overall assessment in the unit. This assignment is an individual one and should be your own work. Timeframe and Submission: A copy of your report must be uploaded no later than 11:59 pm on Sunday of Week 8 on the Canvas in assignment section. Unless approval for an extension is given on medical grounds (supported by a medical certificate) there will be a penalty of 10% of the maximum marks per calendar day for late submission of assignments. Although you will be provided with guidance with regard to addressing the assignment tasks, you will need to complete the tasks in your own time. Part I: Can Recycled Materials Be Used in Electrical Devices? Electronic devices contain electric circuits etched into wafers made of silicon. These silicon wafers are sealed with an ultrathin layer or silicon dioxide., in a process known as oxidation. This can be done with either new or recycled or recycled wafers. In a study described in the book Statistical Case Studies for Industrial Process Improvement by V. Czitron and P. Spagon, both new and recycled wafers were oxidized, and the thicknesses of the layers were measured to determine whether they tended to differ between the two types of wafers. Recycled wafers are cheaper than new wafers, so the hope was that they would perform at least as well as the new wafers. Following are 36 thickness measurements (in tenths of a nanometre) for both and recycled wafers. New 90.0 92.2 94.9 92.7 91.6 88.2 92.0 98.2 96.0 91.1 89.8 91.5 91.5 90.0 93.1 88.9 92.5 92.4 96.7 93.7 93.9 87.9 90.4 92.0 90.5 95.2 94.3 92.0 94.6 93.7 94.0 89.3 90.1 91.3 92.7 94.5 Recycled 91.8 94.5 93.9 77.3 92.0 89.9 87.9 92.8 93.3 92.6 90.3 92.8 91.6 92.7 91.7 89.3 95.5 93.6 92.4 91.7 91.6 91.1 88.0 92.4 88.7 92.9 92.6 91.7 97.4 95.1 96.7 77.5 91.4 90.5 95.2 93.1 Page | 4 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Answer the following questions: 1. Construct comparative boxplots for the thickness of new wafers and recycled wafers. 2. Identify any outliers in the redrawn boxplots. Should any of these be deleted? Explain. 3. Are the distributions of thickness skewed, or approximately symmetric? 4. Delete outliers as approximate and compute the mean, median and standard thickness for new and recycled wafers. 5. Suppose that it is desired to use the type of wafer whose distribution has less spread. a. Write a brief paragraph that explains which types of wafer to use and why. b. Which measure is more useful for spread in this case, the standard deviation or the interquartile rangers? Part II: Can Recycled Materials Be Used in Electrical Devices? The following table is a life table which is used by Life Insurance companies to determine how much to charge for life insurance policies. United States Life Table, Total Population Age Interval Proportion Surviving 0 - 10 0.99123 10 - 20 0.99613 20 - 30 0.99050 30 - 40 0.98703 40 - 50 0.97150 50 - 60 0.94010 60 - 70 0.86958 70 - 80 0.70938 80 - 90 0.42164 90 - 100 0.12248 The column labelled “Proportion Surviving” gives the proportion of people alive at the beginning of an age interval who will still be alive at the end of the age interval. For example, among those currently age 20, the proportion who will still be alive at age 30 is 0.99050 or 99.050%. Answer the following questions: 1. From the table, find the conditional probability P(Alive at age 20 | Alive at age 10) 2. Find the probability that a person aged 20 is still alive at age 100. 3. Find the probability that a person aged 50 is still alive age 70. 4. Which is more probable, that a person aged 20 is still alive at age 50, or that a person aged 50 is still alive at age 60? 5. A life insurance company sells term insurance policies. These policies pay $100,000 if the policyholder dies before age 70 but pay nothing if a person is still alive at age 70. If a person buys a policy at age 40, what is the probability that the insurance company does not have to pay? Page | 5 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Marking Information: The mid-semester test will be marked out of 100 and will be weighted 20% of the total unit marks. Marking Criteria Not satisfactory (0-49%) of the criterion mark) Satisfactory (50-64%) of the criterion mark Good (65-74%) of the criterion mark Very Good (75-84%) of the criterion mark Excellent (85-100%) of the criterion mark Theoretical understanding (20 Marks) All the questions in Part I and Part II are not correctly answered. Some questions are correctly answered but most questions are partially correct. Majority of the questions are correctly answered but significance of the result is not explained Majority of the questions are correctly answered, and significance of the result is explained All questions are correctly answered, and significance of the result is well explained to show its practical relevance. Problem set-up in Excel (30 marks) Fail to set-up problem correctly in excel Problem is correctly set-up but all other relevant information, label and formula syntax is missing. Problem is correctly setup in excel with all relevant information, but formula syntax is missing. Problem is correctly setup in excel; all relevant formulas are shown with correct syntax, but labels are missing Problem is correctly set-up in excel with all relevant information and labels. All relevant formulas are shown with correct syntax Simulation and result (30 marks) No simulation is performed Some part of simulation is correct Most part of the simulations are correct. Correct simulation but minor error in result. Excellent simulation with correct result. Result interpretation (20 marks) No interpretation of result is presented Average interpretation of results; no use of relevant to statistical terminologies; fail to show the implication of result on a given problem Good interpretation of results using relevant to statistical terminologies but fails to show the implication of result on a given problem. Interpretation of results is well presented to using relevant statistical terminologies but fails to show the implication of result on a given problem. Excellent interpretation of results using relevant to statistical terminologies; show the implication of result on a given problem. Page | 6 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Assessment 3: Log/Workbook

Page | 1 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Unit Code and Title: SBM3103 Mathematics and Statistics Assessment Overview Assessment Task Weighting Due Length ULO Assessment 1: Quiz In this assessment task student will sit for online quiz in week 3. This is an individual assignment. 10% Week 3 30 minutes [ULO1] Assessment 2: Case Study In this assessment task student will analyse data collected from a business case. This is an individual assignment. 20% Week 7 1000 words [ULO1], [ULO2], [ULO3], [ULO4] Assessment 3: Log/Workbook This assessment task is a weekly recording of the inside gained through a series of tutorial exercises. This is an individual task. Please find on Canvas for detailed description. 30% Weekly (Week 1 to Week 10) 15 hours tutorial work [ULO1], [ULO2], [ULO3], [ULO4] Assessment 4: Statistical Data Analysis In this assessment task students will perform statistical data analysis based on a data set provided. The data can be downloaded from Canvas under the Assessment 4 Task. This assessment task is an individual task. 40% Week 12 2000 Words [ULO1], [ULO2], [ULO3], [ULO4] Assessment Details Page | 2 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Assessment 1: Quiz Due date: Week 3 Group/individual: Individual (In class during tutorial session) Word count / Time provided: 30 minutes Weighting: 10% Unit Learning Outcomes: [ULO1] Assessment Details: Quiz questions will be based on the materials covered in lectures and tutorials as well as those assigned in these sessions. Quiz questions will be similar to tutorial questions and will require use of a calculator. Multiple choice, short answer questions and quantitative problems may be included in the quiz. Marking Information: The quiz will be marked out of 100 and will be weighted 10% of the total unit marks. Page | 3 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Assessment 2: Case Study Due date: Week 7 Group/individual: Individual Word count / Time provided: 1000 Words Weighting: 20% Unit Learning Outcomes: [ULO1], [ULO2], [ULO3], [ULO4] Assessment Details: The SBM3103 assessment task 2 is worth of 20% of the overall assessment in the unit. This assignment is an individual one and should be your own work. Timeframe and Submission: A copy of your report must be uploaded no later than 11:59 pm on Sunday of Week 8 on the Canvas in assignment section. Unless approval for an extension is given on medical grounds (supported by a medical certificate) there will be a penalty of 10% of the maximum marks per calendar day for late submission of assignments. Although you will be provided with guidance with regard to addressing the assignment tasks, you will need to complete the tasks in your own time. Part I: Can Recycled Materials Be Used in Electrical Devices? Electronic devices contain electric circuits etched into wafers made of silicon. These silicon wafers are sealed with an ultrathin layer or silicon dioxide., in a process known as oxidation. This can be done with either new or recycled or recycled wafers. In a study described in the book Statistical Case Studies for Industrial Process Improvement by V. Czitron and P. Spagon, both new and recycled wafers were oxidized, and the thicknesses of the layers were measured to determine whether they tended to differ between the two types of wafers. Recycled wafers are cheaper than new wafers, so the hope was that they would perform at least as well as the new wafers. Following are 36 thickness measurements (in tenths of a nanometre) for both and recycled wafers. New 90.0 92.2 94.9 92.7 91.6 88.2 92.0 98.2 96.0 91.1 89.8 91.5 91.5 90.0 93.1 88.9 92.5 92.4 96.7 93.7 93.9 87.9 90.4 92.0 90.5 95.2 94.3 92.0 94.6 93.7 94.0 89.3 90.1 91.3 92.7 94.5 Recycled 91.8 94.5 93.9 77.3 92.0 89.9 87.9 92.8 93.3 92.6 90.3 92.8 91.6 92.7 91.7 89.3 95.5 93.6 92.4 91.7 91.6 91.1 88.0 92.4 88.7 92.9 92.6 91.7 97.4 95.1 96.7 77.5 91.4 90.5 95.2 93.1 Page | 4 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Answer the following questions: 1. Construct comparative boxplots for the thickness of new wafers and recycled wafers. 2. Identify any outliers in the redrawn boxplots. Should any of these be deleted? Explain. 3. Are the distributions of thickness skewed, or approximately symmetric? 4. Delete outliers as approximate and compute the mean, median and standard thickness for new and recycled wafers. 5. Suppose that it is desired to use the type of wafer whose distribution has less spread. a. Write a brief paragraph that explains which types of wafer to use and why. b. Which measure is more useful for spread in this case, the standard deviation or the interquartile rangers? Part II: Can Recycled Materials Be Used in Electrical Devices? The following table is a life table which is used by Life Insurance companies to determine how much to charge for life insurance policies. United States Life Table, Total Population Age Interval Proportion Surviving 0 - 10 0.99123 10 - 20 0.99613 20 - 30 0.99050 30 - 40 0.98703 40 - 50 0.97150 50 - 60 0.94010 60 - 70 0.86958 70 - 80 0.70938 80 - 90 0.42164 90 - 100 0.12248 The column labelled “Proportion Surviving” gives the proportion of people alive at the beginning of an age interval who will still be alive at the end of the age interval. For example, among those currently age 20, the proportion who will still be alive at age 30 is 0.99050 or 99.050%. Answer the following questions: 1. From the table, find the conditional probability P(Alive at age 20 | Alive at age 10) 2. Find the probability that a person aged 20 is still alive at age 100. 3. Find the probability that a person aged 50 is still alive age 70. 4. Which is more probable, that a person aged 20 is still alive at age 50, or that a person aged 50 is still alive at age 60? 5. A life insurance company sells term insurance policies. These policies pay $100,000 if the policyholder dies before age 70 but pay nothing if a person is still alive at age 70. If a person buys a policy at age 40, what is the probability that the insurance company does not have to pay? Page | 5 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Marking Information: The mid-semester test will be marked out of 100 and will be weighted 20% of the total unit marks. Marking Criteria Not satisfactory (0-49%) of the criterion mark) Satisfactory (50-64%) of the criterion mark Good (65-74%) of the criterion mark Very Good (75-84%) of the criterion mark Excellent (85-100%) of the criterion mark Theoretical understanding (20 Marks) All the questions in Part I and Part II are not correctly answered. Some questions are correctly answered but most questions are partially correct. Majority of the questions are correctly answered but significance of the result is not explained Majority of the questions are correctly answered, and significance of the result is explained All questions are correctly answered, and significance of the result is well explained to show its practical relevance. Problem set-up in Excel (30 marks) Fail to set-up problem correctly in excel Problem is correctly set-up but all other relevant information, label and formula syntax is missing. Problem is correctly setup in excel with all relevant information, but formula syntax is missing. Problem is correctly setup in excel; all relevant formulas are shown with correct syntax, but labels are missing Problem is correctly set-up in excel with all relevant information and labels. All relevant formulas are shown with correct syntax Simulation and result (30 marks) No simulation is performed Some part of simulation is correct Most part of the simulations are correct. Correct simulation but minor error in result. Excellent simulation with correct result. Result interpretation (20 marks) No interpretation of result is presented Average interpretation of results; no use of relevant to statistical terminologies; fail to show the implication of result on a given problem Good interpretation of results using relevant to statistical terminologies but fails to show the implication of result on a given problem. Interpretation of results is well presented to using relevant statistical terminologies but fails to show the implication of result on a given problem. Excellent interpretation of results using relevant to statistical terminologies; show the implication of result on a given problem. Page | 6 Asia Pacific International College Pty Ltd. Trading as Asia Pacific International College 55 Regent Street, Chippendale, Sydney 2008: 02-9318 8111 PRV12007; CRICOS 03048D Assessment 3: Log/Workbook

Task 1

(a): Frequency Distribution

Occupational Category

Frequency

Management

55

Sales

38

Clerical

97

Se

83

Professional

105

Other

156

Descriptive Statistics

Column1

Mean

4.14794

Standard Error

0.071653

Median

4

Mode

6

Standard Deviation

1.6558

Sample Variance

2.741675

Kurtosis

-0.92965

Skewness

-0.49087

Range

5

Minimum

1

Maximum

6

Sum

2215

Count

534

(b) Relative frequency table

Occupational Category

Frequency

Relative Frequency

Management

55

0.10299

Sales

38

0.07116

Clerical

97

0.18165

Service

83

0.15543

Professional

105

0.19663

Other

156

0.29213

(c) Bar Chart

(d)

X

1

2

3

4

5

6

P(X)

0.10

0.07

0.18

0.16

0.20

0.29

(e)

Let X denote the event

(i) P(X=2) = 0.07

(ii) P( X > 2)= 0.18 + 0.16 + 0.20 + 0.29 = 0.83

(iii) P( X ≥ 3) =0.18 + 0.16 + 0.20 + 0.29 = 0.83

Task 2

(a) Frequency Distribution

union membership

Frequency

0

438

1

96

Column1

Mean

0.179775

Standard Error

0.016633

Median

0

Mode

0

Standard Deviation

0.38436

Sample Variance

0.147733

Kurtosis

0.800367

Skewness

1.672538

Range

1

Minimum

0

Maximum

1

Sum

96

Count

534

(b) Relative frequency table

Union Membership

Frequency

Relative Frequency

0

438

0.82

1

96

0.18

(c ) Bar Chart

(d) Probability Distribution

X

0

1

...

SOLUTION.PDF## Answer To This Question Is Available To Download

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