Quantitative Methods – I June 2026 Solved Assignments

Description

NMIMS

Quantitative Methods – I

APPLICABLE FOR SEM 2 (JUNE 2026 EXAMINATION)

Q1. After surveying a sample of 100 new students, the university finds that 40 indicate a preference for Chinese food. The student affairs office wants to determine if this marks a meaningful shift from prior years’ 30% rate, guiding future dining options. They require a clear, defensible statistical decision process rather than relying on intuition or anecdote. How should the university use z-scores and standard error calculations to identify whether the proportion of students preferring Chinese food in the new batch is significantly different from the historic 30%? Outline the steps and justify the statistical choices involved. (10 Marks)

Ans 1.

Introduction

The institution wants to know whether the 40% preference for Chinese cuisine among incoming students is a statistically significant change from the 30% historical average. An objective and justifiable foundation for making decisions is provided by a formal hypothesis test that uses z-scores for proportions instead of depending on intuition. By using this method, the institution can determine whether the observed difference is the result of random sampling variance or really represents a shift in student preferences.

Q2 (A). A large retail chain uses a contingency table to analyze the shopping habits of its customers based on gender and number of purchases per week. Despite initial insights from joint and marginal probabilities, the management is debating how much attention should be paid to conditional probabilities for segmenting targeted marketing campaigns. There is also internal disagreement whether the events (gender and number of purchases) are independent or not, especially when tailoring cross-selling strategies. This decision impacts both budget allocation and the accuracy of campaign targeting. Critically evaluate the advantages and limitations of relying on marginal, joint, and conditional probabilities for customer segmentation in this scenario. Assess whether assuming independence or dependence between gender and purchasing behavior improves decision-making, and justify which approach the retail chain should adopt for optimal campaign effectiveness. (5 Marks)

Ans 2(A).

Introduction

An organized method for obtaining insights utilizing marginal, joint, and conditional probabilities is provided by the retail chain’s usage of a contingency table to examine buying behaviors across gender and purchase frequency. The true difficulty, however, is determining which probability measure should be used to drive segmentation and whether gender and 

Q2 (B). A national retail chain operates 250 stores across different regions. The average monthly sales per store follow a normal distribution with a mean of $150,000 and a standard deviation of $20,000. Management wants to estimate the probability that a randomly selected store generates monthly sales exceeding $180,000. The results will be used to assess how realistic their premium store classification target is. Using the normal distribution framework: 1. Calculate the probability that a store earns more than $180,000 in a month. 2. Interpret the result in a managerial context. 3. Based on your findings, comment on whether the premium classification threshold appears too strict or reasonable. (5 Marks)

Ans 2(B).

Introduction

The retail chain wishes to assess the viability of its “premium store” benchmark of $180,000 in monthly sales. Standard normal (z) distribution methods may be used to assess the issue since shop sales have a normal distribution with a mean of $150,000 and a standard deviation of $20,000. This enables management to determine if the benchmark is feasible and calculate the percentage of stores anticipated to surpass the goal.