This document outlines an assignment for a business statistics course given to a group of 3 MBA students at Build Bright University in Cambodia. The assignment layout lists statistics problems extracted from a textbook for the students to solve. It provides the student names, contact information, and assigned problem numbers and pages. The problems cover topics such as qualitative vs quantitative variables, population mean and standard deviation, probability distributions, normal distributions, and binomial distributions. Solutions to some of the problems are also provided.
Applichem case discusses about Supply Chain issues related to Market fluctuations in exchange rate and an optimal SC model for a Global setup. In this presentation, our group has analyzed the optimal solution through simplex LP and checked its robustness in event of market exchange rate fluctuations.
This slideshow was created to showcase the marketing research involved in the strategic decision-making process. This presentation represents a decision for the marketing team at Barco Projection Systems, on how to combat the incoming Sony 1270 projector model. This presentation includes a brief history, situation analysis, options for Barco, and an ultimate decision based on this research. This Powerpoint presentation was completed for a Marketing Management & Strategy course.
Cola Wars - Coke Vs Pepsi Harvard Business School Case StudyMohan Kanni
A brief presentation on case study Cola Wars where we try to analyse the past history and predict the future of their business and growth opportunities from a Marketing Management Perspective.
Applichem case discusses about Supply Chain issues related to Market fluctuations in exchange rate and an optimal SC model for a Global setup. In this presentation, our group has analyzed the optimal solution through simplex LP and checked its robustness in event of market exchange rate fluctuations.
This slideshow was created to showcase the marketing research involved in the strategic decision-making process. This presentation represents a decision for the marketing team at Barco Projection Systems, on how to combat the incoming Sony 1270 projector model. This presentation includes a brief history, situation analysis, options for Barco, and an ultimate decision based on this research. This Powerpoint presentation was completed for a Marketing Management & Strategy course.
Cola Wars - Coke Vs Pepsi Harvard Business School Case StudyMohan Kanni
A brief presentation on case study Cola Wars where we try to analyse the past history and predict the future of their business and growth opportunities from a Marketing Management Perspective.
The Espresso Lane to Global markets is the Marketing management case. The power point is an attempt to analyse the case and bring useful suggestions to the company.
Challenges
Inaccurate forecasts of retailer demand has become a major issue at Obermeyer. The two major factors that made this task more difficult was the increase in product variety and intense competition in market. Second challenge the company had faced was to allocate production between Hong Kong and China. Although Obermeyer had 1/3 of Parka production in China for 1992, this year the organization insisted on increasing the sales to half. There was difference in quality and labor rate at China and Hong Kong which made allocation decision more difficult.
Another challenge the company faced was the larger lead time. The company had supplies of raw materials from various countries which resulted in delayed production time. Organization challenges along with competition from competitor companies were major challenges the company had faced.
Analysis
From the sales predictions that the six managers forecasted, a coefficient of variation (COV) was determined, which indicated the level of spread of the forecasted data. The COV values were broadly divided into two levels, the low risk group and the high risk group. Every value below 0.2 were considered to be among the lower risk items and all the items above COV value of 0.2 were considered to be of higher risks. Once the risk levels of each item were determined, the quantities of items to be produced in first and second production cycles could be calculated with least risk. 70% of the entire sales forecast for the lower risk items were ordered to be produced. Only 30% of higher risk items were ordered to be produced in the first production cycle. The quantities which amounted to 1200 were manufactured in China and that which were close to 600, were manufactured in Hong Kong in the first production cycle.
Once the 80% of the orders were received from the retailers from the Vegas show, a clear picture of the demand forecast could be obtained, according to which the rest of the items could be manufactured either in China or Hong Kong. Referring to exhibit 1, the four products to be produced in China in the first production cycle are: Assault, Seduced, Entice and Electra. These four products have COV less than 0.2. However Gail, Daphne, ISIS, Anita, Teri, Stephanie are produced in Hong Kong for the first production cycle as they have a high level of risk associated with it.
Conclusion
Short term operational changes
o Decrease lead time by obtaining raw materials from geographically closer locations to ensure timely delivery
Long term operational changes
o Cross scaling Chinese labors which would help the company produce quality and reliable goods at a cheaper price
Presentation on "Advertising Plan of Nestle Milkpack Re-Launch" by Dr.Syed Ahmed Owais, Shahzad Naseem & Zaheer to Sir.Shahzeb Abbasi in Advertising class given at Hamdard University City Campus, (HIMS).
References:
Advertising Principles & Practice, 7 th edition, Wells, Moriarty, Burnet.
Websites of Nestle, Olpers and Goodmilk.
Crafting winning strategies in a mature market - US wine marketSaurabh Arora
The Industry Landscape in 2001
US: 4th largest wine producer in the world
US: 34th in world per capita wine consumption
Top 8 firms produce more than 75% of all the wine volume
Estimated 2500 firms produce the remaining 25%
Dominance of few large players in the low price market
Greater shelf space & high marketing budget
1990s: Consolidation of retailers and distributors across US
No of distributors fell from 5000 to 250 by 2000
Only 50 to 100 left with access to widespread national distribution
Large retail consolidation in US
Top 10 supermarkets control 55% of the US market in 2000
Majority of producers are focused on low volume/high price to gain maximum return/margin
Distributors are focused on high volume/low price to maximize economies of scale
Near impossible for a new company to establish itself
Low barriers invite more players to wine market
Porter’s five forces analysis
Threat of new entrants – HIGH
Low barriers to entry for new players in wine industry
Firms spent 40% of their expenditures on marketing and distribution
Existing rivalries in industry – HIGH
Total no of wineries in US increased by more than 400%
Glut of grape supply due to low growth in demand
This put downward pressure on price and margins
Bargaining power of Buyers – HIGH
More players are entering the market
Production outstripped demand by 20%
Consolidation of retailer and distributor
Bargaining power of Suppliers – LOW
Wine producers with their own vineyards attempts to control the operations starting from production to distribution
Threat of Substitutes – LOW for Budget
Only 10% people drank wine regularly
Of the remaining 90%, 46% preferred beer or spirits
35% drank alcoholic beverages other than wine
The Espresso Lane to Global markets is the Marketing management case. The power point is an attempt to analyse the case and bring useful suggestions to the company.
Challenges
Inaccurate forecasts of retailer demand has become a major issue at Obermeyer. The two major factors that made this task more difficult was the increase in product variety and intense competition in market. Second challenge the company had faced was to allocate production between Hong Kong and China. Although Obermeyer had 1/3 of Parka production in China for 1992, this year the organization insisted on increasing the sales to half. There was difference in quality and labor rate at China and Hong Kong which made allocation decision more difficult.
Another challenge the company faced was the larger lead time. The company had supplies of raw materials from various countries which resulted in delayed production time. Organization challenges along with competition from competitor companies were major challenges the company had faced.
Analysis
From the sales predictions that the six managers forecasted, a coefficient of variation (COV) was determined, which indicated the level of spread of the forecasted data. The COV values were broadly divided into two levels, the low risk group and the high risk group. Every value below 0.2 were considered to be among the lower risk items and all the items above COV value of 0.2 were considered to be of higher risks. Once the risk levels of each item were determined, the quantities of items to be produced in first and second production cycles could be calculated with least risk. 70% of the entire sales forecast for the lower risk items were ordered to be produced. Only 30% of higher risk items were ordered to be produced in the first production cycle. The quantities which amounted to 1200 were manufactured in China and that which were close to 600, were manufactured in Hong Kong in the first production cycle.
Once the 80% of the orders were received from the retailers from the Vegas show, a clear picture of the demand forecast could be obtained, according to which the rest of the items could be manufactured either in China or Hong Kong. Referring to exhibit 1, the four products to be produced in China in the first production cycle are: Assault, Seduced, Entice and Electra. These four products have COV less than 0.2. However Gail, Daphne, ISIS, Anita, Teri, Stephanie are produced in Hong Kong for the first production cycle as they have a high level of risk associated with it.
Conclusion
Short term operational changes
o Decrease lead time by obtaining raw materials from geographically closer locations to ensure timely delivery
Long term operational changes
o Cross scaling Chinese labors which would help the company produce quality and reliable goods at a cheaper price
Presentation on "Advertising Plan of Nestle Milkpack Re-Launch" by Dr.Syed Ahmed Owais, Shahzad Naseem & Zaheer to Sir.Shahzeb Abbasi in Advertising class given at Hamdard University City Campus, (HIMS).
References:
Advertising Principles & Practice, 7 th edition, Wells, Moriarty, Burnet.
Websites of Nestle, Olpers and Goodmilk.
Crafting winning strategies in a mature market - US wine marketSaurabh Arora
The Industry Landscape in 2001
US: 4th largest wine producer in the world
US: 34th in world per capita wine consumption
Top 8 firms produce more than 75% of all the wine volume
Estimated 2500 firms produce the remaining 25%
Dominance of few large players in the low price market
Greater shelf space & high marketing budget
1990s: Consolidation of retailers and distributors across US
No of distributors fell from 5000 to 250 by 2000
Only 50 to 100 left with access to widespread national distribution
Large retail consolidation in US
Top 10 supermarkets control 55% of the US market in 2000
Majority of producers are focused on low volume/high price to gain maximum return/margin
Distributors are focused on high volume/low price to maximize economies of scale
Near impossible for a new company to establish itself
Low barriers invite more players to wine market
Porter’s five forces analysis
Threat of new entrants – HIGH
Low barriers to entry for new players in wine industry
Firms spent 40% of their expenditures on marketing and distribution
Existing rivalries in industry – HIGH
Total no of wineries in US increased by more than 400%
Glut of grape supply due to low growth in demand
This put downward pressure on price and margins
Bargaining power of Buyers – HIGH
More players are entering the market
Production outstripped demand by 20%
Consolidation of retailer and distributor
Bargaining power of Suppliers – LOW
Wine producers with their own vineyards attempts to control the operations starting from production to distribution
Threat of Substitutes – LOW for Budget
Only 10% people drank wine regularly
Of the remaining 90%, 46% preferred beer or spirits
35% drank alcoholic beverages other than wine
This is an example of a logical step on a statistical investigation. A group of students as research team came up with a problem statement, did data gathering, presented and analyzed the data and then interpreted the results...
I heard about this contest from this website, as I have had uploaded my Cyprus education presentation months ago.
Multi Objective Optimization of PMEDM Process Parameter by Topsis Methodijtsrd
In this study, MRR, SR, and HV in powder mixed electrical discharge machining PMEDM were multi criteria decision making MCDM by TOPSIS method. The process parameters used included work piece materials, electrode materials, electrode polarity, pulse on time, pulse off time, current, and titanium powder concentration. Some interaction pairs among the process parameters were also used to evaluate. The results showed that optimal process parameters, including ton = 20 µs, I= 6 A, tof = 57 µs, and 10 g l. The optimum characteristics were MRR = 38.79 mm3 min, SR = 2.71 m, and HV = 771.0 HV. Nguyen Duc Luan | Nguyen Duc Minh | Le Thi Phuong Thanh ""Multi-Objective Optimization of PMEDM Process Parameter by Topsis Method"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23169.pdf
Paper URL: https://www.ijtsrd.com/engineering/manufacturing-engineering/23169/multi-objective-optimization-of-pmedm-process-parameter-by-topsis-method/nguyen-duc-luan
Fundamental Analysis and Analyst Recommendations - China RailwayBCV
Fundamental Analysis & Analyst Recommendations - China Railway
Thematic Investments: China Railway
Rapid & Efficient Transportation Supports China's Ascent
INVESTMENT RATIONALE
* The length of China’s rail network is planned to reach a total track length of 120'000 km under the current five-year plan, from 20'000 km in 1949.
o The People’s Republic of China boasts the world’s third-longest railway network behind the USA and Russia.
o China is the only country in the world that has significantly expanded its railway infrastructure in recent years and is poised to build it out further in the future.
* Rapid & efficient transportation systems underpin China’s social and economic development.
o By the end of 2011, the People's Republic of China had a total urban population of 700 million or 53% of total population, rising from 26% in 1990.
+ The train is China's main means of transportation. With a population of just under 1.34 billion and a population density of 140/km², China is facing ever-growing transportation needs.
+ The massive ongoing rural exodus is a major challenge for China’s intercity transportation system.
o Rapid economic growth requires efficient transportation systems.
+ The expansion and rationalization of railways (dedicated freight lines) will boost China’s productivity by enabling raw materials and manufactured goods to reach their destination faster and more economically.
* Expanding and upgrading its railway system allows China to address many of its transportation problems, as the rail offers speed, reliability, and cost efficiency (low per-unit transportation costs) on the largest scale possible.
o Despite a temporary halt caused by the 2011 train wreck, the great railroad expansion will resume chugging forward as the social and economic significance of an efficient railway system is key for China's future
o The government's goal is to dramatically increase the speed and efficiency of intercity links, while expanding the current railway network inland to Western countries, therefore creating new efficient trade routes.
o The expansion and building of railroad infrastructure is likely to give companies operating in the railway industry full order books in the years ahead.
o Alongside rail construction companies, rolling stock manufacturers and maintenance, transport and technology firms can also partake in the government’s expansion plans.
Spark-ITS: Indexing for Large-Scale Time Series Data on Spark with Liang ZhangDatabricks
Massive amounts of time series data continuously generated and collected calls for the development of distributed large scale time series data processing platforms. Indexing plays a critical role in speeding up time series similarity queries on which most of these systems rely. However, the state-of-the-art techniques, including the widely adopted iSAX-based indexes, fall short in leveraging the parallel power of modern distributed systems to efficiently construct an index over billions of time series data (TBs of data).
We propose an indexing framework based on Apache Spark, which is composed by a novel index tree, and the related new signature, to index and query billion-scale time series. This framework is composed of a global centralized index and local distributed indexes. This new index not only reduces the depth and the size of the index tree significantly, but also maintains the similarity relationship more effectively compared to existing techniques. We conducted extensive experiments on both synthetic and real-world datasets.
Evaluation results demonstrate that over a 1.0 Billion time series dataset, the construction of un-clustered index is about 60% faster than the state-of-the-art systems, whereas the construction of clustered index is 83% faster than the state-of-the-art systems.
Moreover, the average response time of Exact-Match queries is decreased by 50%, and the accuracy of the kNN-Approximate queries has increased from 3% to 40% compared to existing techniques.
I presented these slides at a meeting of ACM data mining group. I discuss using data mining to improve performance of an existing trading system. The presentation was video taped. You can see the video at:
http://fora.tv/2009/05/13/Michael_Bowles_Neural_Nets_and_Rule-Based_Trading_Systems
if you have any questions or comments contact me: mike@mbowles.com or
http://www.linkedin.com/in/mikebowles
EENG 3305
Linear Circuit Analysis II
Final Exam
December 14, 2013
Name:
Answer the questions in the spaces provided on the question sheets. If you run
out of room for an answer, continue on the back of the page. Please complete
the exam in pencil and clearly denote the final answer. Except where trivial,
show all work!
Question Points Bonus Points Score
1 10 0
2 5 0
3 5 0
4 5 0
5 5 0
6 10 0
7 10 0
8 4 0
9 6 0
10 10 0
11 5 0
12 10 0
13 5 0
14 10 0
15 0 8
16 0 7
Total: 100 15
EENG 3305 Final Exam - Page 1 of 11 December 12, 2013
1. [10 points] Determine the Fourier coefficients a1, a2, a3, a4 and b1, b2, b3, b4 of the rectified
cosine wave shown below
−2 2 4 6 8 10 12
2
4
t
f(t)
EENG 3305 Final Exam - Page 2 of 11 December 12, 2013
2. [5 points] If the rectangular pulse shown below is applied to the circuit, also shown
below, find v0 at t = 1s.
1 2 3
2
4
6
t
vs(t)
+
−vs(t)
2 Ω
2 Ω 1 H
+
−
v0
Page 2
EENG 3305 Final Exam - Page 3 of 11 December 12, 2013
3. [5 points] Find the transfer function
Io(ω)
Is(ω)
for the following circuit
is(t) 2 Ω 1 H 4 Ω
i0(t)
Page 3
EENG 3305 Final Exam - Page 4 of 11 December 12, 2013
4. [5 points] Obtain the Fourier Transform of the following function
−4 −1 1 4
−2
2
t
vs(t)
Page 4
EENG 3305 Final Exam - Page 5 of 11 December 12, 2013
5. [5 points] Use the convolution integral to find e−2tu(t) ∗ e−3tu(t)
6. [10 points] Given that the circuit is initially at rest use the Laplace transform to solve
the differential equation
d2v(t)
dt2
+ 12
dv(t)
dt
+ 35v(t) = e−2t
.
Page 5
EENG 3305 Final Exam - Page 6 of 11 December 12, 2013
7. For the circuit below
+
−60u(t)
2 Ω
+ −
vo(t)
2 H 2 Ω
(a) [2 points] Write the integrodifferential equation for vo(t) assuming no initial condi-
tions in the circuit.
(b) [2 points] Convert the equation you obtained in the previous part to the Laplace
domain.
(c) [2 points] Find the transfer function if the output of interest is the 1Ω resistor
voltage.
(d) [2 points] Calculate the impulse response of the system.
(e) [2 points] Calculate the step response of the system.
Page 6
EENG 3305 Final Exam - Page 7 of 11 December 12, 2013
8. A circuit consisting of a coil with inductance 10mH and resistance 20Ω is connected in
series with a capacitor and a generator with an RMS voltage of 120V. Find:
(a) [2 points] the value of the capacitance that will clause the circuit to be in resonance
at 15kHz
(b) [2 points] the current through the coil at resonance
9. The circuit parameters for a series RLC bandstop filter are R = 2kΩ, L = 1H, C = 40pF.
Calculate
(a) [2 points] the center frequency
(b) [2 points] the half-power frequencies
(c) [2 points] the quality factor
Page 7
EENG 3305 Final Exam - Page 8 of 11 December 12, 2013
10. [10 points] Find the y parameters for the following circuit
4 Ω 6 Ω
ix
2 Ω
3ix
11. [5 points] A balanced delta-connected load has line current Ia = 5 −30◦A. Find the
ph ...
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Khóa luận tốt nghiệp Quản trị kinh doanh: Đánh giá hoạt động quản trị rủi ro lãi suất cho vay tại ngân hàng thương mại cổ phần Quân đội - Chi nhánh Huế cho các bạn làm luận văn tham khảo
Impact of communities' livelihood resulting from ls2 dam resettlement projectNarith Por
Abstract: The demand of energy in Cambodia increased. There are potential natural resources in Mekong River for hydropower dam development that can generate energy to support Cambodia country. Lower Sesan San II project has been constructed and the people of the five villages have been relocated and have planned to be relocated to new sites. This was reason of the research was proposed with topic of “Impact of Communities' Livelihood Resulting from Lower Sesan 2 Hydropower Dam's Resettlement Project” with two objectives: (1) to compare the change of livelihood conditions between pre-resettlement and post-resettlement communities when considering the interrelations of water, food and energy and (2) to determine whether the community is satisfied with the relocation. The research was conducted in Sre Sranuk village with random sampling of 58 people for interview and 10 people for group discussion. The quantitative and qualitative data were used in the research. Table, diagram and t-tests tools were used in data analysis. Research findings were that the livelihood of relocated people changed in comparison of pre-resettlement and post-resettlement due to differences of community resources. The satisfaction of relocated people on community resources, incomes and expenses in pre-resettlement and post-resettlement was based on community resource types, sources of incomes and expenses. The recommendation include support more rice, skill, forest areas for CF establishment, location of budget for CF establishment, spiral areas, inclusion of local people in conflict resolution, well repairing, guarantee of houses for relocated people.
Analysis of institutional capacity of national social protection policy frame...Narith Por
Abstract- Cambodians are still vulnerable. To reverse those conditions, National Social Protection Strategy (N.S.P.S) was developed for the poor and vulnerable people to promote their livelihoods. Royal Government of Cambodia (R.G.C) has paid attention on social assistance. In strategic plans, it highlights on strengthening, and developing social security in collective way, consistent and effectively. With these issues, the government establish national social protection policy framework in order to help all people in particular poor and vulnerable people (M.o.E.F, 2017, p.1). The research aims at reviewing an institutional capacity of government institutions in charge of National Social Protection Framework (N.S.P.P.F) toward its goal achievement” The Department for International Development (D.E.F.I.D) capacity approach is proposed to framework for this institution of government toward its goal achievement. The D.E.F.I.D (2003) cited in Kay & Franks (2003) identifies thee approach for assessing capacities in three level.
The strengths and the weakness of the seven points were identified. Those included Overview of N.S.P.P.F, financial resources, relationship with others, policies and systems, strategies, structures and technical skills and competencies. It was concluded that limitation of budget, lack of data and guideline for implementing the frameworks. Recommendations were identification of People with Disability (P.W.D) data, people close to the poverty line, inclusion of P.W.D, increase in budget and budget decentralization.
1. Stung Treng Campus, Cambodia
MBA Program, Promotion I
ASSIGNMENT
Subject: Business Statistics
Lectured by TepVuthy
Group Members:
1. Por Narith
2. Chor Menglon
3. Loeur Sopheaktra
Due date: 21st August 2011
Build Bright University, Stung Treng Campus, MBA, Promotion I, Group 3: Por Narith, Chor Menglon, Loeur Sopheaktra
2. ACADEMIC YEAR 2010– 2011
Layout of Assignment
The code numbers and page numbers of the problems are extracted from Business Static Book
authored by AMIR D. ACZEL. The problems or exercises are for group 3.
Group Student’s Name Exercise Page Contact
Number Number Number
1-Por Narith 1-6 20 Phone : 012 371 003
1-63 63 E-mail :
3. 2-10 78 narith_por01@yahoo.com
2-23 83
3-9 127
3-14 135
4-3 186
4-17 187
4-38 198
2-Chor Menglon 4-47 199 Phone : 017 920 000
4-54 201
5-1 215
5-15 228
5-22 228
6-20 261
6-28 261 Phone : 077 333 262
3- Loeur Sopheaktra 6-44 265
6-48 307
7-22 261
7-16 305
Build Bright University, Stung Treng Campus, MBA, Promotion I, Group 3: Por Narith, Chor Menglon, Loeur Sopheaktra
3. Solution
Problem 1.6
What is difference between a qualitative and a quantitative variable?
Resolution 1.6
The difference between a qualitative and a quantitative variable included
Qualitative Variable Quantitative Variable
A qualitative or categorical variable simply A quantitative variable can be described by a
record a quality. numbers of which arithmetic operations such
as averaging making sense.
If a number is used for distinguishing
members of different category of a qualitative
variable, the number assignment is arbitrary.
Problem 1.63
The following data are the numbers of tons shipped weekly across the pacific by shipping
company.
398, 412, 560 476, 544, 690, 587, 600, 613, 457, 504, 477, 530, 641, 359, 566, 452, 633, 474
499, 580, 606, 344, 455, 505, 396, 347, 441, 390, 632, 400, 582
Assume these data represent an entire population. Find the population mean and population
standard deviation.
Resolution 1.63
a. Find the population mean
X Observation X-X bar
X1 398 11382.2
X2 412 8590.97
X3 560 3059.47
X4 476 822.973
X5 544 1545.47
X6 690 34340.7
X7 587 6775.35
X8 600 9084.47
X9 613 11731.6
X10 457 2274.1
X11 504 0.47266
X12 477 766.598
X13 530 640.723
X14 641 18581.1
X15 359 21224.8
X16 566 3759.22
X17 452 2775.97
Build Bright University, Stung Treng Campus, MBA, Promotion I, Group 3: Por Narith, Chor Menglon, Loeur Sopheaktra
4. X18 633 16464.1
X19 474 941.723
X20 499 32.3477
X21 580 5671.97
X22 606 10264.2
X23 344 25820.5
X24 455 2468.85
X25 505 0.09766
X26 396 11813
X27 347 24865.3
X28 441 4056.1
X29 390 13153.2
X30 632 16208.5
X31 400 10959.5
X32 582 5977.22
Total 16150 286053
N 32
Sum(X1: X32) 16150
Mean= --------------------------------=-----------------= 504.689
N 32
Σ(X- )2 286053
Std= √---------------= √--------------= √9227.51= 94.547
N 32
Problem 2.10
The European version of roulette is difference from the US version in that the European
roulette wheel doesn’t have 00. How does this change the probability of winning when you bet
on a single numbers? European casino charge a small administration fee, which is not the case
in US casinos. Does this make sense to you based on your answer to the earlier question?
Resolution 2.10
Given that a US casino roulette wheel has 38 slots (00 and 0.36), the odds of landing on a bet
from a single number comes out to be 1 in 38 (or about 2.6%).
Percentage is found by dividing 1 (the numbers of chances you have to get your numbers) by
the numbers of outcome possible (in this case 38)
= 1/38= 0.026316
Problem 2.23
A firm has 550 employees; 380 of them have had at least some college education, and 412 of
the employees underwent a vocational training program. Future more, 357 employees both are
college-educated and have had the vocation training educated or has had the training. If
employee is chosen at random, what probability that he or she is college educated or has had
the trainings or both?
Build Bright University, Stung Treng Campus, MBA, Promotion I, Group 3: Por Narith, Chor Menglon, Loeur Sopheaktra
5. Resolution 2.23
n= 550
P(A): the probability of employees who have had at least some college education.
380
P(A)= ---------------=69.09%
550
The probability of employees who have had at least some college education is 65%.
P(B)= the probability of the employees who underwent a vocational training program.
412
P(B)= ---------------=74.91%
550
The probability of the employees who underwent a vocational training program is 75%.
The probability that he or she is college educated or has had the trainings both include
357
P(A B)=--------------------= 64.91%
550
P(AUB)=(P(A)+P(B))- P(A B)= ((69.09%+74.91%)-64.91%)= 79.09%
The probability that he or she is college educated and has had the trainings includes 79.09%.
Problem 3.9
Return on investment oversee, especially in Europe and the Pacific Rim, are expected to be
higher than those of US market in the near term, and analysis are now recommending
investment international portfolios. An investment consultant believes that the probability
distribution of return (in percent a year) on one such portfolio is as follows:
X(%) P(X)
9 0.05
10 0.15
11 0.3
12 0.2
13 0.15
14 0.1
15 0.05
a. Verify that P(x) is a probability distribution
b. What is the probability that returns will be at least 12%?
c. Find the cumulative distribution of returns
Resolution 3.9
The probability distribution of return (in percent a year) on portfolio is as follows:
Build Bright University, Stung Treng Campus, MBA, Promotion I, Group 3: Por Narith, Chor Menglon, Loeur Sopheaktra
6. X(%) 9 10 11 12 13 14 15
P(X) 0.05 0.15 0.30 0.20 0.15 0.10 0.05
a. A distribution is said to be probability distribution if it satisfies the following condition
P(X) ≥ 0 and ∑P(X) = 1
x
From the above distribution, we can see that are greater than zero and
∑P(X) = 0.05+0.15+0.30+0.20+0.15+0.10+0.05= 1
x
Since the above distribution satisfies both conditions, this is probability distribution.
b. The probability that returns will be at least 12% is
P(X≥12)= P(X=12)+ P(X=13)+ P(X=14)+ P(X=15)= 0.20+0.15+0.10+0.05= 0.5
c. The cumulative distribution of returns is given by
X(%) 9 10 11 12 13 14 15
P(X) 0.05 0.15 0.30 0.20 0.15 0.10 0.05
F(X) 0.05 0.20 0.50 0.70 0.85 0.95 1.00
Problem 3.14
An automobile dealership records the numbers of cars sold each day. The data is used in
calculating the following probabilities distribution of daily sales: Find the mean, variance,
standard deviation of the numbers sold
Resolution 3.14
x P(x) xP(x) x2P(x)
0 0.1 0 0
1 0.1 0.1 0.1
2 0.2 0.4 0.8
3 0.2 0.6 1.8
4 0.3 1.2 4.8
5 0.1 0.5 2.5
Mean of x= 2.8 Mean of x2= 10
a. The mean of numbers of the cars sold each day
E(x)= ΣxP(x)
= > E(x)= 2.8
Average numbers of the cars sole each day is 2.8.
b. Find variance
V(X) = E(x2)-[E(x)]2 = 10-(2.8)2= 2.16
= > Variance= 2.6
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7. The square of deviation from the mean of the cars sold per day is 2.16.
c. Find standard deviation
SD(X) = [V(X)]1/2= [2.6]1/2= 1.47
= > SD(X) = 1.47
The deviation from the mean of the cars sold per day is 1.47.
Problem 4.3
Find the probability that standard normal random variable will have a value between -2.50 and
-0.89.
Resolution 4.3
P (-2.50<Z<-0.89)
P (0<X<2.50) = 0.4938
P (0<X<0.89) = 0.3133
P (-2.50<X<-0.89) = P (0<Z<2.50) - P (0<Z<0.89)
= 0.4938- 0.3133=0.1805 or 18.05% -2.50 -0.89
The probability of the Z value is between -0.89 and -2.50 is 18.05%
Problem 4.17
Find z such that P (Z>z) = 0.12
Resolution 4.17
P (Z>z) = 0.12
So p(Z <z) =0.88
z = 1.174987
z=1.174987
Problem 4.38
If X is a normally distributed random variable with mean 120 and standard deviation is 4.4,
find a value x such that the probability that X will be less than x is 0.56.
Resolution 4.38
x= µ± Z*σ
µ= 120
σ= 44
P(X<x) =0.56
P(X<x)=0.50+0.06
P(X<x)= 0.06=> Z⋲0.16
P(X<x)=0.5= > Z⋲ 6
P(X<x)=0.56= > Z⋲ 6+0.16= 6.16
x = 120± (6.16)*44= 391.04
0.16
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8. Problem 4.47
The demand for unleaded gasoline at a service station is normally distributed with mean
27,009 gallons per day and standard deviation 4,531. Find two values that will give a
symmetric 0.95 probability interval for the amount of unleaded gasoline demand daily.
Resolution 4.47
µ= 27,009 gallon
σ=4,530
95%
P= 0.95%= >Z= 1.96
X= µ± Z*σ
X=27,009 ± 1.96*4530
X=27,009± 8,878.8
X= [18,130.2; 35887.8]
0.95 probability internal for the amount of unleaded gasoline demand daily is between
18,130.2 and 35887.8.
Problem 4.54
A computer system contains 45 identical microchips. The probability that any microchip will
be in working order at a given time is 0.80. A certain operation requires that at least 30 of the
chips be in working order. What is the probability that the operation will be carried out
successfully?
Resolution 4.54
n= 45
p=0.80
q=1-0.80=0.20
X=30
Binominal distributions in which n are large can be approximated using the normal
approximation. So if X is a binominal random variable with parameter p, then:
X-np
Z=-------------------
√np(1-p)
Where the mean of a binomial variable is np and variance is np(1-p), so in this problem p=0.8,
n= 45, np =36 and np(1-p)=7.2
The probability that the operation will be carried out successfully is given by
1
X- np 30+------ - 36
2
P (X≤30) = P (-------------------≤------------------------ (for the normal approximation)
√np(1-p) √7.2
The continuity correction factor of ½ is included
P(X≤30) = 0.0202
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9. Problem 5.1
Discuss the concepts of parameter, a sample statistic, an estimator, and an estimate. What are
the relations among these entities?
Resolution 5.1
Sample statistic is a numerical measurement of sample. Population parameter is the numerical
measurement of population. Estimator of population parameter is a sample statistic used to
estimate parameter. An estimate of a parameter is a particular numerical value of estimator
obtains by sampling. When a single value is used as estimate, the estimate is called the point
estimate of the population parameter.
Problem 5.15
Under what conditions is the central limit theorem most useful in sampling to estimate the
population mean?
Resolution 5.15
The conditions that the central limit theorem is most useful in sampling to estimate the
population mean includes
We need to know population standard deviation (σ).
If, the population standard deviation (σ) is not known, it is replaced with estimator,
sample standard deviation (S).
Problem 5.22
An economist wishes to estimate the average family income in a certain population. The
population standard deviation is known to be $4,500, and the economist uses a random sample
of size n=225. What is the probability that the sample mean will fall within $800 of the
population mean?
Resolution 5.22
σ= 4500
n= 225
µ= 800
The sample mean will fall within $800 of the population mean 81.648%
So, X1= µ-400= 800- 400= 400
X2= µ+400= 800+ 400=1200
X1- µ 400- 800
Z1= -------------------= ----------------------------= - 4/3
(σ/√N) 4500/√225
X2- µ 1200- 800
Z2=------------------= --------------------------= 4/3
(σ/√n) 4500/√225
P (-4/3) = 0.4082
P (4/3) = 0.4082
= > P (-4/3<Z<4/3) = 0.4082+ 0.4082=0.81648
The probability that the sample mean will fall within $800 of the population mean is 81.648%.
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10. Problem 6.20
The manufacture of batteries used in small electrict appliances wants to estimate the average
life of battery. A random sample of 12 batteries yields = 34.2 hours and s=5.9 hours. Give
95% confidence of interval for the average life of batery.
Solution 6.20
n= 12
=34.2
95%
s= 5.9
Confidential 95%= > Z= 1.96
σ
± Z* -------------
√s 1.96
-1.96
5.9
= 34.2 ± 1.96*-----------------------= [30.86, 37.54]
√12
95% confidence of interval for the average life of batery is between 30.86 and 37.54 hours.
Problem 6.28
To aid in planning the development of a tourist shopping area, a state agency wants to estimate
the average dollar amount spent by a tourist in an existing shopping area. A random sample of
56 tourists gives =$258 and s= $85. Give a 95% confidence interval for the average amount
spent by a tourist at the shoping area
Resolution 6.28
n= 56
= 258
95%
s= 85
Confidence of 95%= > Z= 1.96
σ
±Z* -------------
√s
-1.96 1.96
85
= 258±1.96*-------------= [235.74, 293.74]
√56
95% confidence interval for the average amount spent by a tourist at the shoping area is
between 235.74$ and 293.74$.
Problem 6.44
A recent article describes the success of business schools in Europe and the demand on that
continent for MBA degree. The article reports that a survey of 280 European business position
resulted in the conclusion that only one-seventh of the position of MBAs at European business
are currently filled. Assuming that this numbers are exacted and that the sample was randomly
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11. chosen from the entire population of interest, give a 90% confidence interval for the proportion
of filled MBA position in Europe.
Resolution 6.44
p*q
p± Zα/2*√------------
n
l 90%
90% confidence = > Z= 1.64
n= 280
1
Success case= -----*280= 40
7 1.64
-1.64
40
p= ---------=14%
280
q=1-0.14= 86%
0.14*0.86
0.14± 1.64*√--------------------= = [10.6%, 17.4%]
280
90% confidence interval for the proportion of filled MBA position in European is between
10.6% and 17.4%.
Problem 6.48
Before launching its Buyers’ Assurance Program, American Express wanted to estimate the
proportion of cardholders who would be interested in this automatic insurance coverage plan.
A random sample of 250 American Express Card holders was selected and sent questionnaires.
The result was that 121 people expressed interest in the plan. Give a 99% confidence interval
for the proportion of all interested American Express cardholders.
Resolution 6.48
99% confidence= > Z= 2.58
n=250
Success case=121
Success Case 121 99%
= >p=------------------------------= ---------------=48.4%
n 250
q=1-p = 1- 0.484= 51.6%
p*q
p± Zα/2*√------------
n -2.58 2.58
0.484*0.516
0.484± 2.58*---------------------------= [40.25%, 56.55%]
250
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12. 99% confidence interval for the proportion of all interested American Express cardholders is
between 40.25% and 56.55%.
Problem 7.16
An automobile manufacturer substitutes a different engine in cars that were known to have an
average miles-per-gallon ratting of 31.5 on the highway. The manufacturer wants to test
whether the new engine changes the miles-per-gallon rating of the automobile model. A
random sample of 100 trial runs gives x-bar=29.8 miles per gallon and s=6.6. Using the 0.05
level of significance, is the average miles-per-gallon ratting on the highway for cars using the
new engine different from the ratting for cars using the old engine?
Resolution 7.16
µ =31.5
n=100
X-bar=29.8
s=6.6
α =0.05
An automobile manufacturer substitutes a different engine in cars that were known to have an
average miles-per-gallon ratting of 31.5 on the highway
We want to test whether the new engine changes the miles-per-gallon rating of the automobile
model.
Null hypothesis
H0= the average miles-per-gallon rating on the highway for cars using the new engine is not
significantly different from the ratting for cars using the old engine.
H0= µ= 31.5 mpg
Alternative Hypothesis
H1= the average miles-per-gallon rating on the highway for cars using the new engine is
significantly different from the ratting for cars using the old engine.
H1= µ≠31.5 mpg
The level of significance, α= 0.05
A random sample of 100 trial runs give X-bar = 29.8 mpg and s =6.6
α/2= α/2=
Under H0, the test statistic is given by 0.025 0.025
X-bar- µ0 29.8-31.5 Z=- Z0=- Z0=1.
Z=---------------=-------------------=- 2.58 2.58 1.96 96
σ/√n 6.6/√100
As the Z value is in the lower rejection area, H0 is rejected. The given data provides strong
evidence to conclude that the average miles-per-gallon ratting on the highway for cars using the
new engine is significantly different from the ratting for cars using the old engine.
Problem 7.22
Average total daily sales at a small food store are known to be $452.80. The store’s
management recently implemented some changes in displays of goods, order within aisles, and
other changes, and it now wants to know whether average sales volume has changed. A
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13. random sample of 12 days show X-bar= $501.9 and s= $65.00. Using α = 0.05, is the sampling
result significant? Explain
Resolution 7.22
µ0=452.80
n=12
X-bar=501.90
s=65
α=0.05
It was supposed to test the average total daily sales has changed from $452.8 or not.
H0= the average total daily sales has not changed from 452.8
µ0= $452.8
H1= the average total daily sales have changed from $452.8.
µ0≠ $452.8
The level of significance, α= 0.05
The test statistic is
X-bar - µ
t= -------------------------
s√n
501.90-452.80
t =--------------------------------=2.62
65/√12
P-value of the test = 2P (T>2.62) = 0.024
Since the P-value is less than the significance level, α=0.05, we reject the null hypothesis.
Hence, we may conclude that the average total daily sales have changed from $452.8.
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