MIP2602 ASSIGNMENT 4 2025 – STEP-BY-STEP CALCULATIONS PROVIDED (DUE 15 AUGUST 2025)

Description

MIP2602 Assignment 4 Memo | Due 15 August 2025. Step by Step Calculations provided.

SECTION A: PROBABILITY
QUESTION 1
1.1 A bag contains a total of 10 marbles: 3 red marbles, 4 blue marbles, 2 green marbles, and 1 yellow marble.
1.1.1 If one marble is randomly drawn from the bag, what is the theoretical probability of drawing: 1.1.1.1 A red marble = ____________ 1.1.1.2 A blue marble = ____________ 1.1.1.3 A green marble = ____________ 1.1.1.4 A yellow marble = ____________
(4)
1.1.2 Conduct an experiment where you draw one marble at a time from the bag and record the colour, returning it each time. Repeat this 14 times. Use the table below to track your results:
(7)
1.1.3 Based on the results you found in question 1.1.2, calculate the experimental probability for each colour: 1.1.3.1 P(Red) = ____________ 1.1.3.2 P(Blue) = ____________ 1.1.3.3 P(Green) = ____________ 1.1.3.4 P(Yellow) = ____________
(4)
1.1.4 How do the theoretical and experimental probabilities compare in your results? Mention one reason why they might be different. (2)
1.2 One letter is selected at random from the word STATISTICS. What is the probability that the letter is:
1.2.1 S (2) 1.2.2 E (2) 1.2.3 T or C (3)
1.3 A jar contains 4 red, 5 yellow, and 6 blue marbles. Two marbles are drawn one after the other with replacement. Determine the probability that:
1.3.1 Neither marble is red. (2) 1.3.2 The first is blue and the second is yellow. (2) 1.3.3 Both are yellow. (1)
1.4 Two fair dice (one white, one red) are rolled simultaneously. The total of the two faces is recorded. What is the probability that: 1.4.1 The total is 9. (2) 1.4.2 The total is less than 5. (2) 1.4.3 The total is greater than or equal to 10. (2)
1.5 The table below shows the qualifications of 120 hospital staff across departments.
1.5.1 What is the probability that a randomly selected staff member: 1.5.1.1 Works in the surgery department, given they have a degree (3) 1.5.1.2 Has either a diploma or works in the admin department (3)
1.5.2 Which qualification level appears to be most common among staff in the Surgery department? Support your answer with numbers. (2)
1.5.3 What might the data suggest about the qualification trends in the admin department compared to the ER? (2)
1.6 Using information in 1.5, draw a probability tree diagram to represent the process of randomly selecting a staff member from the hospital, identifying their department, and determining their qualification level. (12)
(It is acceptable to start with either the department or qualification but ensure that the branches are accurate.)
1.7 Use the tree diagram you drew in 1.6 to answer the following question:
1.7.1 Which combination has the highest joint probability of selection? Explain why. (2)
1.7.2 Suppose the hospital is planning a training programme for diploma holders. Which department should they prioritize, and why? (2)
[59]
_________________________________________________________________________________________
SECTION B: Ethical and Professional Practices in Data Handling and Analysis
Question 1: Ethical Guidelines in Data Collection and Analysis (6 marks)
1.1 Define the following ethical principles and give one example of how each applies in a research or survey context: 1.1.1 Informed Consent (2) 1.1.2 Transparency (2) 1.1.3 Integrity and Objectivity (2) Question 2: Professionalism in Statistical Practice (21 marks)
2.1 Briefly describe the role of each of the following in ensuring professional data analysis: 2.1.1 Accuracy (2) 2.1.2 Attention to Detail (2) 2.1.3 Confidentiality (2) 2.2 Give an example of professional misconduct in statistical reporting and explain its potential impact. (2) 2.3 Scenario: A health analyst misinterprets units. 2.3.1 What is the risk in healthcare? (1) 2.3.2 Why is unit checking critical? (1) 2.3.3 Suggest one tool/practice to detect such errors. (1)
2.4 Below is a list of usernames and a similar list that might contain typos, extra spaces, or incorrect characters. Carefully compare each pair and indicate whether they are identical or different. If different, circle the part that’s incorrect. (10)
Question 3: Ethical Use of Technology in Statistics Education (10 marks)
3.1 Define the digital divide and explain how it might create inequity in learning statistical tools.
(3)
3.2 Discuss one benefit and one risk of using AI or machine learning in data analysis for teaching. (3) 3.3 Scenario: AI auto-marks open-ended answers. 3.3.1 Identify two ethical/fairness concerns. (2) 3.3.2 Suggest one way to ensure responsible use. (1) 3.3.3 Why monitor AI systems regularly? (1)
Question 4: Data Privacy and Digital Citizenship (4 marks)
4.1 Scenario: A student uses AI summaries without verifying sources. What are the ethical implications? (2) 4.2 Suggest two ways researchers can ensure data privacy when sharing data. (2)
[41]
_________________________________________________________________________________________
TOTAL: 100