Overview You will undertake several statistical investigations using appropriate software (e.g. Excel) and present your findings in a word processed document.

Business and Marketing Business Mathematics

Coursework

(Statistics and Probability)

Spring Term 2021 – 22

CODE:

Assessment Details:

Hand out Date:

7 February 2022

Submission Date:

18 February 2022

Assessment Duration:

12 days

Instructions:

Prepare a report using an appropriate word processing package e.g. Microsoft Word, to explain

your investigations into the tasks specified in this assessment. Please include appropriate

images and results of the work done (calculations and Excel/Geogebra) to support your reported

findings. Your completed work should be uploaded to study smart in a single word-processed

report.

The maximum mark for this assessment is 56 and will comprise 25% of your overall mark for the

module.

Learning outcomes assessed:

Knowledge and Understanding

KU2: Evaluate the strengths and weaknesses of alternative models, and consequently, of any

conclusions drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation

allowing a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a

problem.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

CODE:

Evidence for Assessment:

Report written using an appropriate software.

Submission Details:

On completion, your report should be uploaded, using only your Student ID, to the Assessment Tab on Study Smart. You must not use your name on the submission, either within the document or as the file name when uploading to TurnItIn. All submissions will be processed utilising TurnitIn and compared with documents on the Internet. Your report needs to be original. If it is believed from the TurnitIn report or otherwise, that your assignment is too similar to another work, you will be asked to explain your report during a live viva. Academic Impropriety:

You are reminded that plagiarism is the unreferenced use of other people’s work or your own previous work. This could include visual images, sound recordings, diagrams, as well as written text. You can however use other people’s work as examples, supporting evidence or inspiration as long as it is referenced appropriately. Academic Impropriety also includes copying or using other people’s work and presenting this as your own. This could include work produced by family members, friends or unknown people on the Internet. If you are guilty of Academic Impropriety you are likely to have your grade for the assignment reduced to zero.

CODE:

Task 1 – Performance in Maths 16 Marks

The Ministry of Education is launching a certain project to encourage High school kids to participate more in Maths. Two schools are involved in the project with their performance over the term collected.

Performance (%)

0-10 10- 20

20- 30

30- 40

40- 50

50- 60

60- 70

70- 80

80- 90

90- 100

School A 14 15 13 10 19 55 40 54 49 46

School B 46 49 54 40 55 19 10 13 15 14

In addition,

• The highest score for both schools is 94%

• The lowest score is 4% for school A and 9% for school B.

Write a short report comparing the data for both schools

• Calculate appropriate measures of location and dispersion

• Discuss the advantages and disadvantages of each measure, with reference to your

data

• Compare both schools and advise the Ministry of Education on which school should

be supported with the funding.

You must include appropriate diagrams to illustrate your report explaining how the choice of the diagrams facilitates comparison between the performances in both schools. You need to use diagrams to compare both schools.

Learning Outcomes Assessed Knowledge and Understanding

KU2: Evaluate the strengths and weaknesses of alternative models, and consequently, of any conclusions

drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

CODE:

Task 2 – Rice Production 12 Marks

Data on rice production is presented in in the Table below:

2018 2019 2020 2021

Seasons Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

Rice Production (tons)

19 59 77 41 21 42 103 24 31 69 107 58 52 103 136 48

Write a report showing the trend in rice production over these 4 years. You report should include:

• A time series graph, with 4 point moving averages and trend line.

• A description in your own words of the observed trend of the sales within the given period

of time.

• An explanation of what the trend line represents and what is the difference between the

values given by the trend line and the observed values.

• A prediction for the sales of the company in 2022.

You need to explain if the prediction made is reliable and what factors could influence this prediction.

Learning Outcomes Assessed Knowledge and Understanding

KU2: Evaluate the strengths and weaknesses of alternative models, and consequently, of any conclusions

drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem.

Key and Employability Skills

KE6: Use a range of IT packages, including calculators, spreadsheets, word processors and skills in the

analysis and solution of business problems.

CODE:

Task 3 – Statistical Distributions 12 Marks

It is common knowledge in a company that 2% of shoes made have an imperfection. Different samples of shoes are to be tested, and in each sample any shoes with imperfections will be rejected before sale. You are to write a report to assess the chances of finding shoes with imperfections in the given samples. Note that the company wants to reduce the number of shoes with imperfections to a particular level.

In your report you must state:

• A suitable distribution to model the number of shoes that have an imperfection and an

explanation of why using such a distribution

• All the assumptions needed to model this situation with the chosen distribution and a

comment on their validity

• Calculations of all the appropriate probabilities considering three different samples, with

appropriate comment on the values of the probabilities and the number of shoes chosen

in the samples.

You need to show all working using appropriate spreadsheets (e.g., Excel) and you need to provide full explanations in your own words.

Learning Outcomes Assessed Knowledge and Understanding

KU2: Evaluate the strengths and weaknesses of alternative models, and consequently, of any conclusions

drawn.

Subject Specific Skills

SS3: Identify, simplify and abstract the underlying mathematical structure of a business situation allowing

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

SS5: Choose and apply appropriate techniques in algebra and calculus in finding a solution to a problem.

Key and Employability Skills

analysis and solution of business problems.

CODE:

Task 4 – Probability 16 Marks

Part A

• What is conditional probability and how does is apply to the multiplication rule?

• What does it mean for events to be mutually exclusive?

• How does the concept of mutual exclusivity relate to the Addition rule?

You need to give full explanation with a good use of examples, diagrams and mathematical formulae. Part B A study is carried out on the purchase intentions of consumers, interested in tablets over a 6- month period. This study included a survey of 3000 consumers with the following information discovered;

• If the consumers who were interested in buying a tablet were effectively buying it within

the considered time frame?

• If the consumers bought a Wi-Fi model or a Wi-Fi + 4G model?

• If the consumers were satisfied with their purchase?

An interview with the consumers was conducted to determine if they effectively bought the tablet, which model they bought and if they were satisfied with their purchase. The results are shown below:

• What is the probability that a consumer decides to buy a tablet and will effectively buy it?

• If we know that a consumer decides to buy a tablet, what is the probability that they will

do so?

• What is the probability that a consumer, after buying a tablet, is satisfied with their

purchase?

• Would the last probability be affected by the fact that the consumer bought a Wi-Fi+4G

model?

Write a report to address the questions above and comment on your findings. You need to:

• use appropriate mathematical formulae and the definitions in Part A

• decide which diagrams you are going to use to describe this problem and explain the

reason for your choice

• give full explanations in your own words and show all your working

Purchased Total Programmed Purchase

YES NO

Programmed Purchase

YES 800 200 1000

NO 400 1600 2000 TOTAL Purchased 1200 1800

Satisfied TOTAL Tablets

YES NO Types of Tablets

Wi-fi + 4G

256 64 320

Wi-fi 704 176 Total satisfied 960 240

Learning Outcomes Assessed

CODE:

Knowledge and Understanding

drawn.

Subject Specific Skills

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

Key and Employability Skills

analysis and solution of business problems.

CODE:

Grade Rubric – Business Mathematics Coursework (Statistics and Probability)

Task 1 – Performance in Maths 16 Marks

0 Marks: Insufficient display of understanding and knowledge I. Measures of Location and Dispersion

1 Mark: One correct measure found with no calculations 2 Marks: Two correct measures calculated with correct calculations shown 3 Marks: All correct measures of location or dispersion calculated with correct calculations shown OR at least two measures of location and one measure of dispersion found with correct calculations. 4 Marks: All measures of location AND dispersion correctly found with correct calculation. II. Advantages and Disadvantages

1 Mark: Attempt at finding an advantage OR Disadvantage of one measure 2 Marks: Advantage and disadvantage stated for at least two measures 3 Marks: Advantages and disadvantages stated for more than two measures (at least one measure of location and one measure of dispersion) 4 Marks: Advantages and disadvantages stated for all measures.

III. Diagram(s)

1 Mark: attempt at drawing an appropriate diagram 2 Marks: At least one correct diagram shown with no explanation 3 Marks: At least one correct diagram shown with some explanation 4 Marks: Correct diagrams shown with clear explanation and explanation of why are appropriate IV. Comparison

1 Mark: Attempt at giving a comparison between both schools 2 Marks: Basic comparison with no or poor explanation 3 Marks: Good comparison with little explanation 4 Marks: Good comparison with clear explanation and address the question on which school should receive the support.

Learning Outcomes Assessed Knowledge and Understanding

drawn.

Subject Specific Skills

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

Key and Employability Skills

CODE:

analysis and solution of business problems.

CODE:

Task 2 – Rice Production 12 Marks

0 Marks: Not enough work to achieve marks

I. Diagram(s)

1 Mark: Attempt at producing a diagram 2 Marks: Correct time series graph with no moving averages nor trend line 3 Marks: Correct time series graph with correct moving averages OR correct trend line 4 Marks: Correct time series graph with correct moving averages AND correct trend line II.

II. Description 1 Mark: Attempt at describing the trend 2 Marks: Basic explanation of the trend with no mention to the trend line 3 Marks: Good explanation of the trend with mention to the trend line 4 Marks: Good explanation of the trend and good description of what trend line represents II

III. Comparison and prediction 1 Mark: Attempt at comparison or prediction 2 Marks: Little explanation of difference between observed values and trend line and no prediction given 3 Marks: Good explanation of difference between observed values and trend line with attempt at prediction. Little explanation on reliability. 4 Marks: Good explanation of difference between observed values and trend line with correct prediction. Clear explanation on reliability with external factors included.

Learning Outcomes Assessed Knowledge and Understanding

drawn.

Subject Specific Skills

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

Key and Employability Skills

analysis and solution of business problems.

CODE:

Task 3 – Statistical Distributions 12 Marks

0 Marks: Not enough work to achieve marks

I. Modelling 1 Mark: Attempt at stating a model for the problem 2 Marks: Correct distribution, poor notation and no or poor explanation 3 Marks: Correct distribution with correct notation and little explanation 4 Marks: Correct distribution with correct notation and good explanation

II. Assumptions 1 Mark: Attempt at stating any assumption 2 Marks: At least one correct assumption with no comments on validity 3 Marks: At least two correct assumptions with basic comment on validity 4 Marks: At least three correct assumptions with good comments on validity

III. Calculations 1 Mark: Attempt at finding at least one probability 2 Marks: Only one sample considered with some calculations and no explanation given 3 Marks: At least two samples considered with calculations and little explanation given 4 Marks: At least three samples considered with calculations and good explanation given

Learning Outcomes Assessed Knowledge and Understanding

drawn.

Subject Specific Skills

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

Key and Employability Skills

analysis and solution of business problems.

CODE:

Task 4 – Probability 16 Marks

0 Marks: Not enough work to achieve marks

I. Conditional Probability and Mutually Exclusive Events 1 Mark: Attempt at giving one of the two definitions 2 Marks: One definition correctly given with an example 3 Marks: Both definitions correctly given with appropriate examples 4 Marks: Both definitions correctly given with appropriate examples and connection explained

II. Diagrams

1 Mark: Attempt at drawing an appropriate diagram 2 Marks: Appropriate possibly not complete diagram(s) with no or poor explanation 3 Marks: Appropriate good diagram(s) with some explanation 4 Marks: Correct appropriate diagram(s) with good explanation

III. Calculation of probabilities

1 Mark: Attempt at calculating a probability from the tables 2 Marks: Correct method to calculate at least one of the required probabilities 3 Marks: Correct calculation of at least two of the required probabilities 4 Marks: All correct probabilities calculated and test if the last probability depends on Wi- Fi+3G

IV. Structure of Report and Justification of Findings

1 Mark: Poorly structured discussion, very few diagrams 2 Marks: Reasonable structure and English, with appropriate diagrams. 3 Marks: Good structure supported throughout by appropriate diagrams and few spelling mistakes. Convincing justifications are given where required 4 Marks: Clear structure supported by good diagrams and no spelling/grammar mistakes. Where required, justification of results is thorough and accurate.

Learning Outcomes Assessed

Subject Specific Skills

a business-related problem to be modelled.

SS4: Solve a range of business-related problems either deterministically or probabilistically as

appropriate.

Key and Employability Skills

analysis and solution of business problems.