K17MA Advanced Mathematics For Science Assignment Task

Published: 06 Jun, 2025
Category Assignment Subject Education
University UCSI University (UCSI) Module Title K17MA Advanced Mathematics For Science

K17MA APPLICATIONS OF STATISTICAL ANALYSIS IN REAL-WORLD PROBLEMS

Statistical analysis is a fundamental tool for understanding and solving real-world problems. Through various techniques such as experimental design, graphical representation of data, probability calculations, and inferential statistics, we can make informed decisions, predict outcomes, and assess risks in diverse fields. By applying statistical methods, we can validate
claims, analyse trends, and estimate parameters that describe complex systems, from scientific studies to business and sports analytics.

K17MA TASK 1: Experimental Design And Inference (5 Marks)

A nutrition research company conducted a study with 25 volunteers to test the effects of a new supplement called “NutriCore” over 3 months. The company reported an improvement in energy levels based on participants’ self-assessment.

Question:

Why can’t we conclude from this study that “NutriCore” increases energy levels for the entire population?
Provide at least two strong statistical reasons related to sample size, bias, or study design.

K17MA TASK 2: Graphical Representation Of Data (10 Marks)

Below is the number of international students studying in the United States from various countries in 2022.

K17MA Advanced Mathematics For Science Assignment

Instructions:

Use Excel to create a bar graph and a pie chart for the data above.
Which chart type better represents this dataset? Justify your answer with at least two reasons.

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K17MA TASK 3: Normal Distribution & Probabilities (30 Marks)

Choose a reliable secondary dataset (e.g., heights, weights, temperatures, incomes) from sources like Kaggle, Data.gov, or UCI Repository.
Use your selected dataset to demonstrate understanding of continuous probability distribution.

Instructions:

  1. Check for normality using graphs or tests (e.g., histogram, Q-Q plot).
  2. Transform the data to standard normal distribution (Z-scores).
  3. Calculate and interpret the probability that a value falls within a specific range.
  4.  Calculate and interpret the confidence interval for the mean.
    Include all calculations, charts, and interpretations.

K17MA TASK 4: Probability And Permutations (15 Marks)

A cybersecurity analyst must guess a secure 6-digit password made of digits 0 to 9 with no repetition.

1. What is the probability of guessing the password correctly on the first try?
2. Assume the company changes the rule:
o Any permutation of the correct 6 digits is accepted.
o The analyst assumes one of the following combinations:

  1. All digits are unique
  2. One digit repeats twice
  3. Two digits repeat twice
  4. One digit repeats three times
    Calculate the probability of guessing the correct 6-digit combination in each case. Show full steps and formula usage.

K17MA TASK 5: Data Collection, Descriptive & Inferential Analysis (40 Marks)

Two NBA teams have been assigned to your group (Refer to the list given). Collect team stats from season 1990-91 to 2024-25 from: https://www.basketball-reference.com/teams/

Instructions:

  1. Example: if one of the team is ‘Atlanta Hawks’ under FRANCHISE click ‘Atlanta Hawks’. You will see there are 76 seasons for this team. Click Share & Export and choose ‘Get as Excel Workbook’ to download the data.
  2. Step 3 to 6 uses only Team 1 data.
  3. Create a stem-and-leaf plot for ‘Wins’. Calculate median and mode. Interpret the results.
  4. Build an ungrouped frequency table for number of wins. Calculate mean, variance, and standard deviation. Interpret the results. Plot a bar graph and pie chart.
  5. Create a discrete probability distribution for ‘Wins’. Give examples for probability. Calculate mean, variance, and standard deviation and interpret the results. Compare with results from step 4 and discuss the results.
  6. Create a grouped frequency distribution for “Wins”. Calculate the mean, median, mode, variance, and standard deviation. Draw a histogram and estimate the mode visually. Draw a cumulative frequency curve and estimate the median visually. Interpret all the results. Compare and discuss your results from step 5.
  7. Construct a binomial distribution for wins and losses of Team 2 in the 2023-24 season. Give a few examples in finding probability. Compute mean, variance, and standard deviation. Interpret all the results.
  8. Construct a Two-Way Classification Table comparing both teams’ wins and losses from the 2022-2023 season.
  9. Using the Two-Way Classification Table:
    (a) Are ‘Wins’ and ‘Team 2’ independent events?
    (b) Are ‘Losses’ and ‘Wins’ mutually exclusive?
    Explain and justify your answers.

K17MA Advanced Mathematics For Science Assignment

Your Investigation Will Be Assessed Using The Following Assessment Design Criteria.

Marking Criteria For K17MA ASSIGNMENT JULY/SEPTEMBER 2024

Concepts and Techniques Reasoning and Communication
A
11-15

Comprehensive knowledge and
understanding of concepts and
relationships.
Successful development and application
of mathematical models to find concise
and accurate solutions.
Appropriate and effective use of
electronic technology to find accurate
solutions to routine and complex
problems.
Comprehensive interpretation of mathematical
results in the context of the problem.
Drawing logical conclusions from mathematical
results, with a comprehensive understanding of
their reasonableness and limitations.
Highly effective communication of
mathematical ideas and reasoning to develop
logical and concise arguments.
B
9-10

Some depth of knowledge and
understanding of concepts and
relationships.
Some development and successful
application of mathematical models to
find mostly accurate solutions.
Mostly appropriate and effective use of
electronic technology to find mostly
accurate solutions to routine and some
complex problems.
Mostly appropriate interpretation of
mathematical results in the context of the
problem.
Drawing mostly logical conclusions from
mathematical results, with some depth of
understanding of their reasonableness and
limitations.
Mostly effective development and testing of
valid conjectures, with substantial attempt at
proof.
C
6-8

Generally competent knowledge and
understanding of concepts and
relationships.
Successful application of mathematical
models to find generally accurate
solutions.
Generally appropriate and effective use
of electronic technology to find mostly
accurate solutions to routine problems.
Generally appropriate interpretation of
mathematical results in the context of the
problem.
Drawing some logical conclusions from
mathematical results, with some understanding
of their reasonableness and limitations.
Development and testing of generally valid
conjectures, with some attempt at proof.
D
4-5

Basic knowledge and some
understanding of concepts and
relationships.
Some application of mathematical
models to find some accurate or partially
accurate solutions.
Some appropriate use of electronic
technology to find some accurate
solutions to routine problems.
Some interpretation of mathematical results.
Drawing some conclusions from mathematical
results, with some awareness of their
reasonableness or limitations.
Some communication of mathematical ideas,
with attempted reasoning and/or arguments.
E
1-3

Limited knowledge or understanding of
concepts and relationships.
Attempted application of mathematical
models, with limited accuracy.
Attempted use of electronic technology,
with limited accuracy in solving routine
problems.
Limited interpretation of mathematical results.
Limited understanding of the meaning of
mathematical results, their reasonableness or
limitations.
Attempted communication of mathematical
ideas, with limited reasoning.

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