MS1S463 Problem Solving for Computing Asynchronous Assessment Brief 2026 | University Of South Wales

MS1S463 Assessment Brief

Assessment Description

Your Task

Complete the five questions in the appendix of this document.

Your report must be typed – handwritten scanned work will not be accepted. You must show all workings, no marks will be awarded for a solution with no appropriate calculations. You should work to 4 decimal places unless specified by the question.

Your work may be uploaded to a plagiarism detector so please ensure that you have not submitted work which would be considered plagiarised from one of your class mates.

Submission

All work must be submitted in accordance with instructions provided by your lecturer.

Guidance On Format Of Assessment

Note: Students are reminded not to include this assignment brief with the assignment submission.

Referencing must be completed in line with the USW Harvard style, as outlined here: https://library.southwales.ac.uk/collections-subject-guides/referencing/

Learning Outcomes Assessed

LO1 Apply a range of problem-solving techniques

LO2 Interpret the solutions to problems appropriately

Marking Criteria/Rubric

Marks available for each question are indicated next to each question.

Note: All grades are provisional until they are ratified by the exam board

Use Of Artificial Intelligence

This section will let you know if and how you can use AI in this assessment. You can also find our handy guides here.

USW AI Assessment Scale (AIAS)

Please note that using AI incorrectly can be considered academic misconduct.

Referencing, Plagiarism And Good Academic Practice

It’s important you learn to reference correctly, and that you adhere to the guidelines of good academic practice.

Submission Details

Ensure that your submission abides by the requirements set out by your lecturer.

University Closure or staff sickness. If there is something about the feedback you have been given that you are unclear about, please see your module tutor.

If you do not submit your assessment or do not effectively claim Extenuating Circumstances, you will receive 0%. This may affect your chances of successfully passing the module. It may also be used as an indicator that you are not engaging on your course.

Appendix 1

MS1S463 – COURSEWORK: 2025-26

Your report must be typed – handwritten scanned work will not be accepted. You must show all workings, no marks will be awarded for a solution with no appropriate calculations. You should work to 4 decimal places unless specified by the question.

Your work may be uploaded to a plagiarism detector so please ensure that you have not submitted work which would be considered plagiarised from one of your class mates.

This coursework is worth 50% of your module and is marked out of 100.

You should attempt all FIVE questions.

1.A regular 4-sided die (a tetrahedron with faces numbered 1,2,3 and 4) and a regular 6-sided die (a cube with faces numbered 1,2,. . . 6) are rolled on a table and the number on the faces in contact with the table surface are added together to create a total value.

(a) Construct a table that shows all possible combinations of total values.

(b) Produce a bar chart representing the frequency of the total values. Hence determine the probability that the sum of the two values is less than or equal to 4.

(c) Determine the mode of the total values.

(d) What is the probability that both dice will have even values on the faces in contact with the table?

(20 marks)

2. The student support services department at a local University records the number of students that are seen each day for 30 consecutive days. The results are given below:

(a) Determine the population mean and population standard deviation of the above data.

(b) Group the above data into classes of 5.5-10.5, 10.5-15.5,. . . and produce a histogram of the grouped data.

(c) Calculate the median of the grouped data.

(20 marks)

3. (a) A local doctors surgery observed that they make one hospital referral on average every 12 hours.
What is the average number of hospital referrals made in a full 24-hour day?
Use the Poisson distribution to calculate the probability that the doctors does not refer any patients to the hospital in a given 24-hour period.
Use the Poisson distribution to calculate the probability that the doctors surgery makes at most two referrals in a given 24-hour day.
Use the Poisson probability to calculate the probability that the Doctors makes at least one patient referral over a 48-hour period.
(b) The time taken for patient arrivals at the doctors surgery is known to be normally distributed with mean µ = 15 minutes and standard deviation σ = 3 minutes.

Find the probability that it takes the patient between 10 and 25 minutes to be seen by the doctor.
Find the probability that it takes the patient less than 12 minutes to be seen by the doctor.
(25 marks)

4. A local convenience store needs to place a long term order on the supply of Milk that can be sourced from one of 3 different Dairy Farmers (A, B and C). However there is a shortage due to tight farmer margins, the high cost of inputs (feed and energy in particular) and logistics are having impact on supply. The overall profit per pint of milk depends availability and input cost factors. With weather prospects for pasture uncertain, farmers are not able to advise on if the current shortage will continue or whether it will subside. The profit that the convenience store will make if they choose each farmer is presented in the table below:

Which manufacturer should be used based on

(i) the maximax criterion,
(ii) the maximin criterion,
(iii) the minimax (a.k.a. regret) criterion, and
(iv) the Laplace criterion?

(16 marks)

5. A research institution wishes to invest in new laboratory equipment to maximise experimental throughput. The equipment will be purchased from two suppliers, A and B; $x$ units will be purchased from A, and $y$ units will be purchased from B. Information about the equipment and the requirements of the research institution are given below:

• Equipment from supplier A costs £5,000 each, while equipment from supplier B costs £12,000 each.
• The institution has a budget of £150,000 to spend on equipment.
• The institution has space for 15 units of equipment in total.
• The institution needs at least 4 units of equipment from supplier A and at least 3 units from supplier B.
• Equipment from supplier B is more advanced than those from supplier A; equipment from supplier A has a limit of 2,000 experiments per hour, while equipment from supplier B has a limit of 4,000 experiments per hour. The overall performance of the entire collection of equipment is approximated by the sum of all the experiments that each individual unit can deliver.

(a) Express the above 4 pieces of information about the equipment and the requirements of the research institution as four inequalities.

(b) Represent these four inequalities on a graph.

(c) Deduce that the expression to be maximized corresponds to $P = 2x + 4y$.

(d) Hence determine the number of units of equipment that should be purchased from supplier A and supplier B that maximizes the overall performance $P$.

(19 marks)

[Total 100 Marks}