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Quantitative Methods (STAT-201)
Assignment 3: Excel QM (Social-Responsible)
2nd Semester, 1444-1445 (2023-2024)
Due date: 06 May 2024 (Time: 11:00 PM)
Student’s Name Student’s ID Section/CRN Location Marking Scheme
Question Score Obtained Score
Q-1 2 Q-2 2 Q-3 2 Q-4 2 Note: You are required to fill your full name, ID, and CRN.
Message: Social responsibility is a framework of ethics in which an individual collaborates and works with other organizations and individuals for the betterment of the community. There are numerous ways in which an organization can exhibit social responsibility; for instance, by promoting volunteerism, facilitating donations, employing ethical employment practices, and implementing environmental improvements. It introduces the subjective obligation that entails maintaining a delicate equilibrium between one’s ecosystem and the economy, as well as the potential compromises that may be made between economic progress and societal and environmental wellbeing. This transcends business organizations and affects all individuals whose actions influence the environment.
Solve the following questions using Excel QM. (2×4 = 8 marks)
1. Helping others through blood donation is a form of social solidarity or social responsibility. The blood donors cite a sense of social responsibility as their reason for donating blood, and as a result, the communities value and reward this activity. The following table shows the number of blood donors in a university from 2011–2023. Develop a 3-year moving average forecast and obtain the related statistical measures using excel QM. year Blood Donors
2011 116
2012 105
2013 146
2014 159
2015 108
2016 194
2017 227
2018 219
2019 234
2020 224
2021 248
2022 253
2023 265
2024 311
Solution:
2. University X has a unique on-campus dispensary that provides medical care. On a typical working day, patients arrive at the dispensary at an average rate of 2 patients per hour. There is one single nurse at the dispensary, and the average time required to give a consultation is 12 minutes.
It is assumed that the service times can be described by the exponential distribution, and the arrival process by a Poisson distribution. You are requested to find:
a. The average time in line,
b. The average number of patients in line,
c. The average time in the system,
d. The average number of patients in the system,
e. The probability that the dispensary is empty,
f. The utilization factor of the system.
Solution:
3. Assume that you are a statistical consultant and want to provide a volunteer consultation to a start-up company as a social responsibility consultation. The company is planning to purchase a uniform outfit for their employees, and they obtained the following quantity discount table with three discount options:
DISCOUNT NUMBER DISCOUNT QUANTITY DISCOUNT COST (SAR)
1 0 to 49 100
2 50 to 99 90
3 100 and over 85
Annual demand is 400 outfits, ordering cost is 50, and holding cost is 25% of the cost of the outfit. Use Excel QM to find the discount option with the minimum total cost.
Solution: 4. To help needy people through charity is a form of social responsibility. The act of doing charity to help others is recognized and rewarded by all communities of the society. The following table shows the amount collected through charity and the amount spent on social development (in million dollars) in the last 8 years. Find the correlation and coefficient of determination for the given data and obtain the related statistical measures using excel QM.
Year Amount collected(y) Amount spent(x)
1 18 15
2 14 10
3 12 9
4 15 12
5 10 5
6 8 4
7 9 6
8 6 3
Solution: