Quantitative Methods – I: NMIMS Internal Assignment Dec 2025 Examination

Quantitative Methods – I

Dec 2025 Examination

Q1. A telecommunications company is piloting a new internet service and surveys 250 randomly selected customers, finding that 162 express interest in subscribing. The marketing analyst is required to estimate, with 90% confidence, the proportion of the entire customer base likely to be interested in the new service. The analyst must apply the correct estimation approach for proportions and ensure the results are suitable for strategic decision-making. In this scenario, how should the marketing analyst apply the interval estimation formula for proportions to determine the confidence interval for the proportion of customers interested in a new service? Explain your reasoning and the steps involved. (10 Marks)

Ans 1.

Introduction

One of the most essential concerns for organisations testing new goods or services is: What percentage of consumers are likely to use it? This issue is very important for a telecoms firm that is launching a new internet service since it directly affects pricing, marketing, infrastructure investments, and long-term profit expectations. If you merely look at a tiny survey or the raw percentage of respondents that are interested, you might be misled. This is because any survey only covers a small part of the whole 

 

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Q2(A). A financial advisory firm tracks client satisfaction rates for three advisors. Initially, the firm uses prior probabilities based on the number of clients per advisor. After a client reports high satisfaction, the firm wants to update the probability that this client was served by each advisor using Bayes’ theorem. The management is debating whether this approach will yield actionable insights for performance evaluation and resource allocation. Assess the appropriateness of applying Bayes’ theorem to revise probabilities in a financial advisory firm where new information about client satisfaction becomes available. What factors should the firm consider to ensure the revised probabilities are meaningful and actionable? Critically justify your evaluation. (5 Marks)

Ans 2A.

Introduction

Bayes’ theorem is a logical way to change your views as you get new information. It is technically correct for a financial advising business that keeps track of customer happiness among three advisers to use Bayes’ theorem to change the chance that a pleased client was handled by a certain advisor. However, whether the new probabilities provide useful information relies on how the priors and likelihoods are set, the quality of the data, and the situation in which the findings are 

Q2(B). A large financial institution is standardizing its risk analysis procedures. Some departments use Excel’s NORM.DIST and NORM.INV functions for normal distribution calculations, while others rely on the traditional z-table. Management is concerned about consistency, accuracy, and the ease of training new analysts. The institution must decide which method to adopt as the standard for all probability calculations. Assess the implications of using Excel’s NORM.DIST and NORM.INV functions versus the traditional z-table for probability calculations in a large financial institution. How should the institution weigh the trade-offs between computational efficiency, accuracy, and interpretability when standardizing probability analysis  across departments? (5 Marks)

Ans 2B.

Introduction

Risk analysis is a key part of how contemporary banks work. Calculating probabilities correctly is important for making important choices like credit risk assessment, portfolio management, value-at-risk (VaR) calculation, and stress testing. Analysts used to use z-tables to figure the cumulative probabilities and percentiles for the standard normal distribution. But in the last several decades, software programs like Microsoft Excel have included built-in functions like NORM.DIST and NORM.INV that