Dear students, get fully solved assignments by professionals
Do send your query at :
or call us at : 08263069601
(Plagiarism proofed assignments available with 100% surety and refund)
Quantitative Methods – I
Dec 2025 Examination
Q1. A call center receives an average of 4 customer complaints per hour. Past records indicate that complaints arrive independently and follow a Poisson distribution. The center operates from 9 AM to 5 PM with 8 working hours per day.
1. What is the probability that exactly 3 complaints will be received in a randomly chosen hour?
2. What is the probability that no complaints will be received in the first hour after opening?
3. Based on your calculations, explain whether it is unusual for the call center to have zero complaints in any given hour. Use probability values to justify your answer in context (10 Marks)
Q2. A manufacturing company produces ball bearings with diameters that are normally distributed, having a mean diameter of 50 mm and a standard deviation of 0.02 mm. For quality control, any ball bearing with a diameter less than 49.97 mm or greater than 50.03 mm is considered defective.
From a day’s production of 10,000 ball bearings:
1. Calculate the expected number of defective ball bearings.
2. Evaluate if the defect rate meets the company’s target of keeping defects below 2%. (10 Marks)
Q3 (A). A machine is designed to fill bottles with 500 ml of juice. A sample of 16 bottles has a mean fill of 495 ml and a standard deviation of 8 ml. At the 5% level of significance, apply an appropriate hypothesis test to determine whether the machine is underfilling bottles. Assume the population is normally distributed. (5 Marks)
Q3(B). A real estate analyst wants to study the relationship between the size of a house (in square meters) and its market price (in Rs. lakhs) using simple linear regression. The following data is collected for 6 houses:
| House | Size (X) in sq. m | Price (Y) in Rs. lakhs |
| 1 | 140 | 85 |
| 2 | 160 | 95 |
| 3 | 170 | 98 |
| 4 | 180 | 102 |
| 5 | 200 | 110 |
| 6 | 210 | 115 |
Task:
1. Calculate the regression equation of Y on X.
2. Using this equation, predict the market price of a house with an area of 190 sq. m. Round all final answers to two decimal places. (5 Marks)
Dear students, get fully solved assignments by professionals
Do send your query at :
or call us at : 08263069601
(Plagiarism proofed assignments available with 100% surety and refund)
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)
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)
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)
Dear students, get fully solved assignments by professionals
Do send your query at :
or call us at : 08263069601
(Plagiarism proofed assignments available with 100% surety and refund)