Quantitative Methods I DEC 2026
Dec 2026 Examination
Q1 A retail chain prided itself on aligning snack offerings with customer preferences, historically finding that 40% of customers favored healthy snacks. After changing suppliers, a sample of 150 recent sales transactions shows a new proportion of healthy-snack purchases. The market research analyst is tasked with evaluating, using statistical methods and z-scores for proportions, whether this change reflects a genuine shift in customer taste or random sampling variation. How should the market research analyst apply z-score formulas for proportions to assess if the adjusted snack assortment aligns with customer preferences, given recent survey results and comparison with established proportions? Provide a framework for the analysis and discuss its practical implications for stock management. (10 Marks)
Ans 1.
Introduction
Retailers have always believed that the 40% of its customers would prefer healthier snacks. This belief came from years of research. In the event of a supplier change this notion needs to be examined again. A sample of 150 recent transactions shows a different percentage of snacks that are healthy. Can this new figure show a real shift in customer perception of food? Is it simply some random change in a regular samples? A z-score test for specific proportions can help
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Q2 (A) A leading e-commerce company is analyzing customer purchase behaviors to optimize inventory. The data science team must ensure that probability concepts such as mutually exclusive, overlapping, and independent events are correctly applied when modeling the likelihood of customers purchasing specific combinations of products. Senior management notices that sometimes probabilities are incorrectly added or multiplied without checking event types, leading to errors in sales forecasting and inventory management. Evaluate the consequences of misapplying the addition and multiplication theorems of probability in the context of this company’s inventory planning. Critically assess how recognizing the distinctions between mutually exclusive, overlapping, independent, and dependent events can improve accuracy in sales forecasts and resource allocation decisions. Justify strategies to avoid these analytical mistakes. (5 Marks)
Ans 2(A).
Introduction
Probability rules appear simple on paper. Take one form of event. Multiply to get another event. In the end, mixing event types will result in incorrect numbers rapidly. Bad numbers lead to poor estimates and stock-buying decisions that are bad.
Concept and Application
mutually exclusive vs. overlapping Events
Event that is mutually exclusive will not happen together. One customer may purchase only one
Q2 (B) An insurance company has designed a life policy where payments to members are made on their 65th birthday and every subsequent 5th year. Historical data shows the average lifespan of policyholders is 67.2 years with a standard deviation of 4.8 years, and lifespan is assumed to follow a normal distribution. Recently, under the normal distribution assumption, the estimated probabilities are that 32.28% of members receive no payment, 28.1% receive two or more payments, and 4.78% receive exactly three payments (between 75 and 80 years lifespan). The policy team is considering whether the interpretation of these statistics is appropriate for financial forecasting and risk management. Critically evaluate the suitability of using the normal distribution assumptions in predicting insurance payouts for this policy. Justify whether the decision-making processes based on these probabilities reflect real-world claim risks and suggest how management could improve their forecasting accuracy given the organizational context. (5 Marks)
Ans 2(B).
Introduction
The insurance company believes that the lifespan is a normal distribution. This assumption drives every payout probability it calculates. The actual data on human lifespan does not necessarily match a perfectly normal curve. The gap is important for financial forecasting.
Concept and Application
Why the Normal Distribution Was Chosen