Today all around the globe, temperatures are rising, seal level is steadily creeping up, and most of the incredible natural beauty is in retreat. While our generation takes these assets for granted, the reality is there is a real possibility that by not acting aggressively that our lives could be changed forever and not in our benefit. With all that said, this allows E227 Global Solutions the opportunity to begin looking toward a brighter and cleaner future where not only our children will be able to live and play happily, but generations to come will have the same opportunities we have all been granted with.
The time is now to begin reducing our carbon footprint by 25% in the next year in order to not only become a more fiscally sound business, but to show our fellow human beings that we care about the environment as much as they do. In order to make this happen, we have begun research looking into brilliant methods that will establish as us leaders in an industry that all businesses will all eventually be catching up to. The three methods we will present you with go as follows: solar energy to reduce electricity, paper/waste reduction, and focusing on green power.
By exercising these options not only will we be reducing our carbon footprint upward of the 25% we anticipate, we will be saving immense amounts of money that will be able to be put into future projects and continue to hire more employees that are held to the same E227 Global Solutions standard. This strategy to go green will not only impress the public and increase our image, but we will be reaping the benefits of lowered operating costs all while doing something to preserve our natural environment. These solutions that are about to be presented should be taken into heavy consideration.
It has come to our attention as of late that this company has become rather wasteful in how it operates. Employees are operating old technology such as computers and continuously leaving them on when they leave for the weekends increasing our energy costs. Paper is being bought and used at an alltime high rate, and we are merely absorbing the cost of others inability to conserve. This is the time to begin implementing 21^{st} century business standards into a business that is still operating like it is stuck in the 20^{th} century.
As a global business we possess a duty to the society and world we work in to become efficient as many others before us have become and many will after. E227 Global Solutions has been fortunate to operate in the treacherous conditions of business and become who it is, but now we owe it the world around us to begin these changes. I have spent some time consulting with the research team and the solutions they have offered have taken cost into strong consideration, and we are certain that within the next year we will already be seeing the positive effects of this decision.
The purpose of this proposal will be the problem/solutions of why our company E227 Global solutions should go green. Will we go over cost, benefits, and any underlying issues we may face by choosing this particular option.
The option that our company, E227 Global Solutions, wants to implement is energy savings. By informing our employees to turn off all electrical components in order to save electricity. We will also be upgrading our equipment like our lights and our old AC machines. By upgrading all the lights to have LED in the building would be a great way to save electricity. By getting rid any of our old machines we will be able to lower our carbine footprint. We have also researched This will be the best option out of the four options because the company will be able to lower the carbine foot print more sufficiently.
The following sources are what we have used in our research. Each are credible sources, the first source on the list is a book providing us with a lot of knowledge in order to provide a wellstructured report. Stating that we can chose to communicate with another company in order to lower our carbine foot print. The second source describes how the use of electricity is broken down. The third source include lots of facts in which we can easily implement that with in our report as well as our company. The fourth source shows the new product in which our company will be implementing so that we can save energy. The fifth source are statistics in what appliance waste energy while they are turned on. The sixth source describes the advantages for using LCD. The seventh source is about how we can implement solar panels so that cost go down seventyfive percent and brings performance up by fifty percent. The eight source is about the average electricity usage per square foot by community are in Chicago. The ninth source is about how a company that replaces heat pumps and how they are beneficial as well. The tenth source shows LG monitors and their cost for each one. The eleventh source shows an exact cost for a 19 inch desktop monitor. The twelve sources describe the exact cost of solar panels. The thirteen sources is about the exact cost of solar panels installments on a house. The fourteen sources is describing AC units and heat pumps that are energy efficient from a company named GE. The fifteen source shows three heat pumps in which also include a description for each one. The sixteen sources show the Carrier Infinity Series heat pumps that include Green Speed Intelligence.
The three parts that our report will consist of are Solutions/Benefits, Costs, and the conclusion. Each part plays an important role of this report. It shows in detail the important factors that lead into in deciding which option would be the most sufficient. In Solution and Benefits we will be presenting each option. Which will be Energy Savings, Waste Management, Green Power, and Saving Paper. In the first option Energy Savings, we will describe how we are going to save energy.
Our companies have looked into the follow options in order lower our carbine foot print which are:
Nowadays it is just impossible to enter in a room and do not see an electronic device plugged in the wall, lights turned on everywhere, Air Condition or Heater on, charges, and several others electronics devices. This is the simple reality we all live today. But, the one thing we do not see when we enter in the room it is the facility required to deliver all that power to our electronics. According to the 2013 ComEd Environmental disclosure statement, the largest electric utility in Illinois, coalfired plants, followed by nuclear plants, are the main power sources in the U.S. Those two sources of energy offer a high environmental risk. Furthermore, deploying a longterm energy conversation plan for our offices would reduce our carbon footprint, and provide considerable savings in our energy utility bills.
Another good point to work on is waste management and recycling. Any place with a group of people generates waste, and most part of the waste generated is recyclable. Most of our waste it is made of materials that are slowly running out in the world or it is a waste that presents some kind of environmental impact. Recycling not just saves our environment of this dangerous waste, but also it generates jobs opportunities for many citizens.
Recycling it is not the only part of this option. Just managing the waste generated by the offices is not enough. We also have to work on in the source, which is the amount of waste generated by the office. Many things as water bottles, plastic bags, Styrofoam boxes.
Green power is one more alternative to reduce the amount of energy used from the big nuclear or coalfire power plants. As the first option, energy savings, this option focus is reducing the amount of energy drain from those not environmental friendly plants, but instead of working on the devices that drains the energy we would be generating our own energy. There are some recent alternatives for generating green energy such as solar panels and wind power. There are several benefits that this option brings as well, such as if we generated more energy than we use we could sell this extra to the energy company.
Paper is made from trees, reducing the amount of paper would direct reduce the environmental impact our company causes. Trees play an important role in our environment by increasing the air humidity, preventing soil erosion, recycling water and controlling the amount of pollution in the air. By saving paper we would be saving the environment, and helping to keep the small portion of our forests, just 5% of what remains (Green Facts, p. 4).
After an intensive research in each one of the options, we decided to go with option 1, Energy Efficiency. This option is the option that presents the best costs vs. benefits in the long run, as will also increase our savings with energy bills. All other options could also reduce severely our carbon footprint, but comparing the downsides of each of them we should go with option 1.
Waste management is a big thing, but in order to waste management and recycling works we would need an additional staff to handle with this waste, separating all waste generated, controlling products bought by the office, and working with the local recycling company.
Green power is something new; many companies are trying to generate their own energy by trying to use wind power or solar panels. The problem with wind power and solar panels is the amount of energy generated by those technologies. Those technologies does not generated enough power for sustaining a whole office, they would generate just part of the energy, and the other part would be pulled from the coalfired or nuclear power plant. An installation that would sustain the office would use an extremely big amount of space, and we would still be dependent of the weather. In a windless or sunless day we would have to use the standard power source. Saving paper is another great thing to do, but this option does not present a good feedback in the long run compared to being Energy Efficiency.
For last, being Energy Efficient would require an initial investment as any of the options require, but this initial invest would pay him self in the long run with savings in utilities bills. In addition this solution is autosuficient, it would not change the company workflow or it would require hiring an additional staff.
Going Green is a great way to reduce our carbon foot print on our planet and can also come with additional perks by saving us money on electricity by replacing any old appliances to energy star or installing L.E.D lights and getting rid of the florescent and new monitors of less energy consumption But these options of course come at a cost. Green appliances such as energy star brands like LG and GE make monitors, heating and cooling systems, even L.E.D lighting, microwaves, and refrigerators for the break room, lighting monitors so when no one is present in a room lights shut off automatically replacing all of these appliances will cost up to LED Samsung LED Essential T8 – 4000K florescent replacement $12.99 while buying in bulk a piece while replacing 63200 lights the cost will be $820,968 According to (EarthLED.com) and a sales rep from (Samsung) which in comparison An Incandescent light uses approximately 3285 kWh/year, which sums $574 dollars for a single light bulb on for one hour – considering the current energy price in Chicago, 1kW costs $0.17 cents. A LED light uses approximately 329 kWh/year resulting in $57 dollars for the same period of time. For computer monitors we can use new computer monitors instead of the old monitor we have that consume 638.3 KWh which runs up to $59.32 a year When we Can use LG Electronics 19″ Smart Energy Saving LED Desktop Monitors with 54.6 Kwh Power which consume $6.84 year are 100.10 dollars apiece but when buying in bulk it cost 89.60 according to (Full Compass) and “LG”. we will need to replace around 1400 which will come up to be $125,440.Central heating and cooling system is better than having offices with ac boxes which can consume more electricity due to amount of units needed which is an estimated 36 which one unit uses 670 kWh which can add up to $1284 a year per unit in total it will come to be $46,224 a year, if we used is a “5 ton Infinity® Heat Pump with Green speed Intelligence” and it cost $4,598 According to (WEBHVAC) with installation we will need 2 which is $9196.00 in order to cool down and conserve more energy 2 of them will ensure equipment from breaking down and maximum performance and with its Green speed Intelligence just set a temperature and it will know when to cool or heat in a green manner the total cost of doing this will be 830289.44 but it uses 2604 kWh which is $5004 a year which is $10,008 a year in total which we save a total of $36216 every year making this an even better method. Automatic wall plug monitor can help us save a lot too but it depends on the work hours we set to our employees as a central monitor controls all of the lighting to power systems in the building this can be set to turn off any lights that it sees no ones in also can turn off any unused appliances that do not need to be on but of course this can be programmed manually and one can set certain time when things will turn off and on, according to (Belkin) there WeMo® Insight Switch which cost 59.99 per unit but in bulk 41.89 one per wall switch thus we will need around 65 in total of $2722.85, this can be our solution in order to automatically turning off unused appliances and also only uses Monitor your electronics’ usage/cost and receive custom notifications Put your electronic devices on a schedule or have them respond to Sunset and Sunrise but this again will save us at least 65 % of our energy consumption by turning off anything unused but it depends on usages so be saving around 19694 kHw a month which adds up to $37,812 back in our pocket every year. According to (NVOCC) shipping specialist in order for us to ship out appliances to Indonesia the total cost will be 21,348.91 the invoice will be displayed below. Replacing old appliances to green appliances will be best to reduce our carbon foot print by consuming less energy and this will also save us money both here and our branch in Indonesia the total amount will add up to $1681927.79 for appliances here and also transported to our Indonesian branch. Over time as the graph show below we will be saving lots of power while also cutting our electric bill by more than half and also saving the branches lots of money by doing this change.
With old appliances used and not turning off any appliances I have come up with the cost of electricity in green. In purple while using the new appliances plus turning off any unwanted wall switch we can save even more electricity and money over the year while using less energy consumption.
The reason for the cost of LED being do high the florescent lighting system has 2 lights in each case in thus causing more lights to be replace.
R A T I N G D E T A I L S  
Ocean Container Rates from Chicago To Jakarta (Indonesia)
Total Volume Weight 32000 lb or 14515.1 kgs.

After intensive research, we strongly recommend Option 1 – Energy Efficiency. When we replace a single pane window in the building with an energyefficient one, the new window prevents heat from escaping in the winter, so we save energy by using our furnace or electric heater less while still staying comfortable. In the summer, efficient windows keep the heat out, so the air conditioner does not run as often and thus we save electricity.
When we replace an appliance, such as a refrigerator, or office equipment, such as a computer or printer, with a more energyefficient model, the new equipment provides the same service, but uses less energy. This saves us money on your energy bill in the long run with little to no maintenance, and reduces the amount of greenhouse gases going into the atmosphere.
The team has unanimously chosen Energy Efficiency with good reason. With all the other options at weigh, we are confident that we have made the best decision in choosing Option 1. The advantages of Energy Efficiency are significantly more favorable in our case being that it not only conserves more energy; it also saves us money and manpower. In comparison to the other options, we strongly believe that we have chosen the most impactful option for the greater good of our company. For further questioning and information please feel free to contact us at:
Rainbow Warriors:
+1 (800)3333333
rainbowwarriors@gmail.com
References:
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To begin with there are several questions regarding the subjective probabilities associated with the eleven possible results. Since five heads will occur more frequently than any other combination, it should be significantly greater than the average value of 9.1%. The assigned value for obtaining five heads is 22%. Since the binomial distribution is symmetric the probability of getting three heads will be the same as the probability of getting seven heads. Knowing that the total number of heads must be between zero and 10 and also that the sum of all the percentages must equal 100% exactly these were assigned a subjective probability of 12%. Again since the binomial distribution is symmetric the probability of getting no heads will be the same as getting all heads. The subjective probability assigned to both of these results was 1%.
From this point the remainder of the subjective probability chart was filled out knowing that the distribution was symmetric, each value had to be between 0 and 1, and the sum of all the probabilities had to be exactly 1. After a little bit of experimentation the table at the top of the following page was generated:
X = Heads  0  1  2  3  4  5  6  7  8  9  10 
Prob (X)  0.01  0.02  0.05  0.12  0.19  0.22  0.19  0.12  0.05  0.02  0.01 
Examination by eye confirms that the distribution is symmetric and each value is within the allowed range. For the final requirement it is readily confirmed that
2 (0.01 + 0.02 + 0.05 + 0.12 + 0.19) + 0.22 = 1.00
and an acceptable subjective probability distribution has been generated.
Assuming that a fair coin is being used, the probability of getting heads on any toss will be 0.50 as will be the probability of getting tails. This means that over an extended period of time half of the tosses are expected to be heads and half of them are expected to be tails. As a result for a total of 600 tosses the expected value for heads is 300. Also since the probabilities of success (heads) and failure (tails) are equal this means that the probability of getting three heads will be exactly equal to the probability of getting three tails. Finally, the probability of getting three heads is exactly equal to the probability of getting seven tails. This is due to the fact that this is a binomial distribution and the only possibilities are heads or tails. If exactly three heads are generated then the other seven tosses must have resulted in tails.
The first graph presented for discussion is a line graph showing the evolution of cumulative heads percentage over all 60 simulations. It would be expected that this cumulative percentage would approach the success probability over a long enough timeline. Since the probability of success in this case (assuming a fair coin) is 0.50 the line graph should approach this value with decreasing fluctuations as the number of simulations increases. This line graph is presented at the top of the following page:
The sharp jump at the beginning simply represents an abundance of heads after a short number of tosses. Around the 25^{th} toss the cumulative probability returned to its expected value and then dipped below 0.50 showing an overall abundance of tails. As expected the line graph continued to fluctuate around 0.50 with the degree of fluctuation decreasing as the total number of simulations increased.
The second graph is a comparison of the subjective probabilities to the computational probabilities calculated. The subjective probabilities can be thought of as a gut instinct while the computational probabilities are exact based on the binomial distribution formula. This graph is presented at the top of the following page:
The subjective probabilities are shown in blue and the computational probabilities are shown in red. For this particular subjective probability distribution the central values were underestimated while the outer values were overestimated. Notice that both distributions are symmetric as would be expected. The overall logic error in the subjective probability distribution appears to be a misunderstanding of how quickly the probability decreases as the number of successes deviates in either direction from the expected value of five. Also notice that the standard deviation of the subjective distribution is larger than that of the computational distribution.
The final graph is a comparison of the empirical probabilities to the computational probabilities. The empirical probabilities are determined from the sixty simulations: empirical probability distributions are expected to approach the computational distribution as the number of trials increases. Again this graph is presented at the top of the following page:
Interestingly enough the empirical distribution also appears to underestimate the computational distribution for the central values and overestimate it for the outer values. Notice here that the empirical distribution is no longer symmetric, and there is no reason to expect that it would be. It appears that sixty simulations are enough for the empirical distribution to be recognizable compared with the computational distribution. In other words the empirical distribution is a reasonable approximation but is not exact.
In conclusion this experiment is very good for showing the differences between the three types of probability distributions. It is simple to execute and the fact that the probabilities of success and failure are equal make the subjective distribution easier to analyze. All three distributions are relatively similar and all of the results were as expected.
APPENDIX A
The first thing that I learned was that there is actually some reasoning that goes into determining a subjective distribution. Before this experiment I felt it was a mostly useless exercise, especially if the computational distribution was readily available. Now I realize that with a bit of logic it is possible and actually not too difficult to generate a reasonable subjective distribution. The advantage of this is that for situations where the computational distribution is more difficult a ballpark idea can be gathered with relative simplicity.
The next thing that I gained from this project is a better interpretation of the line graph for cumulative percentage of heads. I knew that it would approach the expected value, but I never really thought about what the fluctuations really meant. No I understand that when the cumulative probability is greater than the expected value that there is an abundance of successes while when the cumulative probability is less than the expected value there is an abundance of failures. The last thing that I learned was that a relatively small number of simulations can generate a reasonable empirical distribution. With eleven different possible outcomes I would have thought that considerably more than sixty simulations would have been needed.
On a slightly different note I also learned some new functions for the Excel spreadsheets. The most interesting one to me was the command to generate the exact probabilities for a binomial distribution. All the other functions I used were familiar to me, but it was good practice to use them again. I feel like this project helped me learn and reaffirm quite a bit of knowledge related to probability distributions and the use of Excel to analyze them.
APPENDIX B
Toss  Number  Cumulative  Total Coins  Cumulative 
Number  Heads  Number Heads  Tossed  Percent Heads 
1  5  5  10  0.5000 
2  7  12  20  0.6000 
3  5  17  30  0.5667 
4  6  23  40  0.5750 
5  4  27  50  0.5400 
6  7  34  60  0.5667 
7  3  37  70  0.5286 
8  4  41  80  0.5125 
9  6  47  90  0.5222 
10  8  55  100  0.5500 
11  6  61  110  0.5545 
12  5  66  120  0.5500 
13  6  72  130  0.5538 
14  5  77  140  0.5500 
15  3  80  150  0.5333 
16  3  83  160  0.5188 
17  7  90  170  0.5294 
18  5  95  180  0.5278 
19  6  101  190  0.5316 
20  2  103  200  0.5150 
21  6  109  210  0.5190 
22  5  114  220  0.5182 
23  3  117  230  0.5087 
24  2  119  240  0.4958 
25  6  125  250  0.5000 
26  2  127  260  0.4885 
27  8  135  270  0.5000 
28  4  139  280  0.4964 
29  3  142  290  0.4897 
30  7  149  300  0.4967 
31  5  154  310  0.4968 
32  3  157  320  0.4906 
33  4  161  330  0.4879 
34  6  167  340  0.4912 
35  9  176  350  0.5029 
36  5  181  360  0.5028 
37  7  188  370  0.5081 
38  6  194  380  0.5105 
39  4  198  390  0.5077 
40  2  200  400  0.5000 
41  5  205  410  0.5000 
42  8  213  420  0.5071 
43  4  217  430  0.5047 
44  5  222  440  0.5045 
45  5  227  450  0.5044 
46  6  233  460  0.5065 
47  8  241  470  0.5128 
48  7  248  480  0.5167 
49  4  252  490  0.5143 
50  4  256  500  0.5120 
51  0  256  510  0.5020 
52  4  260  520  0.5000 
53  7  267  530  0.5038 
54  6  273  540  0.5056 
55  5  278  550  0.5055 
56  2  280  560  0.5000 
57  3  283  570  0.4965 
58  5  288  580  0.4966 
59  4  292  590  0.4949 
60  7  299  600  0.4983 
Table 1.
Simulation number, Total number of heads, Cumulative number of heads
Total number of coins tossed, Cumulative percentage of heads
Number  Subjective  Actual  Empirical  Computational 
Successes  Probability  Successes  Probability  Probability 
0  0.010  1  0.017  0.001 
1  0.020  0  0.000  0.010 
2  0.050  5  0.083  0.044 
3  0.120  7  0.117  0.117 
4  0.190  10  0.167  0.205 
5  0.220  13  0.217  0.246 
6  0.190  11  0.183  0.205 
7  0.120  8  0.133  0.117 
8  0.050  4  0.067  0.044 
9  0.020  1  0.017  0.010 
10  0.010  0  0.000  0.001 
Sums  1.000  60.000  1.000  1.000 
Table 2.
Number of successes, Subjective probability, Actual successes
Empirical probability, Computational probability
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Introduction
Managers and team leaders are often faced with a myriad of challenges in their daily tasks. They have to find a solution if they will be successful leaders in their companies. In the case of Tim and Kristen, both business leaders are facing difficult choices: Tim must choose between Allesandra and Kristen for the timecompressed casino project; and Kristen must convince her team to sacrifice their vacations in the interest of the company, or risk losing her position. The memo details the real problems and puts forwards recommendations to solve the issues.
Case Overview
To start with, Tim is not the best manager and company leader. Considering the conversations between Kristen and he, it is easy to notice that he fails to communicate productively with his junior manager, Kristen. For example, he does not clearly answer Kristen’s questions regarding the timing of the project. He only introduces the project and says that he trusts her to get her team to execute it. It is also noteworthy that Tim accepted a major project which needed to be implemented in a strict timeline, without consulting his team. Clearly, Tim’s focus is on the task, and has little regard for the feelings and thoughts of his juniors, including Kristen. He has accepted a project but, interestingly, he wants to delegate it to someone. In other words, he does not want to be part of the solution, yet he is quick to judge Kristen’s inability to get her team to work. Perhaps this is one reason he could not get along with the more aggressive Allesandra.
Allesandra is talented and has a way of motivating her team into action. She would possibly find a way to get this major project executed within the given timeline. She has done it before, so she is experienced. In contrast, Kristen does not appear to be as aggressive as her predecessor. However, it is worth noting that the challenge she faces is real: she had approved her team members’ vacations and all of a sudden she is asking them to forget it. The reason her team members are unwilling to make sacrifice for the team is perhaps because she has not cultivated rapport with them. Apparently, they do not see her as one of them. Instead, they perceive her as someone they have to listen to.
Solving the Problem
To solve the problem, it is recommended that Tim gets his hands dirty and leads by example. To this end, he should call Kristen and her team to a meeting. He should then clearly explain the importance of the project at hand, and why it needs to be completed. He should also explain company policy in such times as this. In so doing, Tim must demonstrate strong communication and interpersonal skills so as to convince his juniors to make sacrifices. He should not sound as if he is forcing or threatening the employees to take up the project. For instance, he can make compromises, such as agreeing to make up for the lost holiday time once the project is completed, besides other motivators and rewards that are appropriate in line with the company’s policy. This way, Tim would be able to get the team to execute the task. This would be good for the clients and the company: client needs would be catered for, and Tim would have created precedence in his firm as far as teamwork and sacrifice is concerned.
While the option of hiring Allesandra is attractive as it would ensure that the job is executed properly, it can be detrimental to the company for the future. Kristen and her team would possibly feel sidelined. This could affect execution of future projects, which can badly impact on Driscoll. Such a move can also demotivate employees, including the possibility of talented staff leaving the firm. This is so especially considering that apparently, one of the reasons Allesandra left the company was because she was not getting along with Tim, then her boss.
Conclusion
In conclusion, Driscoll is facing a managerial and teamwork crisis. Tim is failing as a manager, while Kristen needs to do better to cultivate and maintain rapport and teamwork among her team members. Instead of hiring Allesandra, Tim should lead by example in helping Kristen to get her team to work. He should take a chance with his rookie.
]]>A student has an important exam coming up and is contemplating not studying for the exam in order to attend a party with his friends. The student must earn a minimum score of 70% on the exam in order to successfully maintain his desired GPA. Suppose the student knows in advance that the exam will consist of twenty multiple choice questions with four possible answers for each question. Answer questions 13 using the preceding information and modeling this situation as a binomial distribution.
1. What is the probability that the student will successfully earn exactly the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?
o 2.57
o 2.57E02
o 2.57E05
o 2.57E04
2. What is the probability that the student will earn less than the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?
o 0.74673
o 0.85198
o 0.99997
o 0.23499
3. What is the probability that the student will successfully earn no less than the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?
o 3.51E04
o 2.95E05
o 6.87E06
o 1.27E03
The mean time required to complete a certain type of construction project is 52 weeks with a standard deviation of 3 weeks. Answer questions 47 using the preceding information and modeling this situation as a normal distribution.
4. What is the probability of completing the project in no more than 52 weeks?
o 0.25
o 0.50
o 0.75
o 0.05
5. What is the probability of completing the project in more than 55 weeks?
o 0.2743
o 0.5091
o 0.1587
o 0.0546
6. What is the probability of completing the project between 56 weeks and 64 weeks?
o 0.2587
o 0.3334
o 0.5876
o 0.0911
7. What is the probability of completing the project within plus or minus one standard deviation of the mean?
o 0.951
o 0.852
o 0.759
o 0.683
Customers arrive at a supermarket checkout counter with an average arrival rate of 9 customers per hour. Answer questions 810 using the preceding information and modeling this situation as a Poisson distribution.
8. What is the probability of less than 5 customers arriving at the supermarket checkout counter in a given one hour period?
o 0.054
o 0.446
o 0.359
o 0.612
9. What is the probability of exactly 12 customers arriving at the supermarket checkout counter in a given one hour period?
o 0.262
o 0.044
o 0.073
o 0.189
10. What is the probability of no less than 12 customers arriving at the supermarket checkout counter in a given one hour period?
o 0.115
o 0.197
o 0.381
o 0.686
A local commuter bus service advertises that buses run every twelve minutes along a certain route. Answer questions 11and 12 using the preceding information and modeling this situation as an exponential distribution.
11. What is the probability of a bus picking up the passengers at a given bus stop in less than or equal to 12 minutes following their arrival at the bus stop?
o 0.519
o 0.632
o 0.466
o 0.772
12. What is the probability of a bus picking up the passengers at a given bus stop in more than 15 minutes following their arrival at the bus stop?
o 0.287
o 0.343
o 0.541
o 0.119
Scores for a certain exam follow a normal distribution with a mean of 87 and a standard deviation of 4. Answer questions 13and 14 using the preceding information.
13. What is the standard Zscore associated with a score of 89?
o 0.0
o 1.1
o 0.8
o 0.5
14. What is the probability that a randomly selected student’s score will fall between a standard Zscore of 1.5 and a standard Zscore of 1.8?
o 0.599
o 0.682
o 0.761
o 0.897
Use the following data set and assumptions to create payoff and regret matrices in order to answer questions 15 through 18.
Alternative A Alternative B
Present value of costs incurred for selecting the alternative prior to knowing which state of nature actually occurs $7,000,000 $12,000,000
Present value of future revenues if the state of nature that actually occurs favors the selected alternative $75,000,000 $125,000,000
Present value of future recoverable costs if the state of nature that actually occurs does not favor the selected alternative $6,000,000 $5,000,000
Assume that there are four collectively exhaustive alternatives from which you must choose prior to knowing the actual state of nature that will occur.
· Select alternative A
· Select alternative B
· Select both alternatives A and B
· Select neither alternative A nor alternative B
Assume that there are two collectively exhaustive states of nature that could occur.
· The state of nature that occurs favors alternative A.
· The state of nature that occurs favors alternative B.
Assume that the estimated costs associated with selecting a given alternative must be incurred prior to knowing which state of nature will actually occur.
15. What is the payoff if alternative A is selected and the state of nature that occurs favors alternative A?
o $7,000,000
o $0
o $61,000,000
o $68,000,000
16. What is the payoff if alternative B is selected and the state of nature that occurs favors alternative A?
o $7,000,000
o $0
o $61,000,000
o $68,000,000
17. What is the regret if alternative A is selected and the state of nature that occurs favors alternative B?
o $0
o $1,000,000
o $113,000,000
o $114,000,000
18. What is the regret if alternative B is selected and the state of nature that occurs favors alternative A?
o $0
o $1,000,000
o $75,000,000
o $114,000,000
Use the payoff and regret data provided in the following payoff and regret matrices to answer questions 19 through 22.
Payoff Matrix
States of Nature
Alternatives State of Nature Favors A State of Nature Favors B State of Nature Favors Neither A nor B
A $88 ($5) ($5)
B ($8) $156 ($8)
A and B $80 $151 ($13)
Neither A nor B $0 $0 $0
Note: The values in the preceding table are shown in millions of dollars.
Regret Matrix
States of Nature
Alternatives State of Nature Favors A State of Nature Favors B State of Nature Favors Neither A nor B
A $0 $161 $5
B $96 $0 $8
A and B $8 $5 $13
Neither A nor B $88 $156 $0
Note: The values in the preceding table are shown in millions of dollars.
19. What is the optimal decision regarding which alternative to select using the Expected Monetary Value decision rule, assuming the probability of the state of nature that favors alternative A occurring is 0.50, the probability of the state of nature that favors alternative B occurring is 0.30, and the probability of the state of nature that favors neither location A nor location B occurring is 0.20?
o Alternative A
o Alternative B
o Alternative A and B
o Neither Alternative A nor Alternative B
20. What is the optimal decision regarding at which location(s) to purchase property using the Expected Opportunity Loss decision rule, assuming the probability of the state of nature that favors alternative A occurring is 0.50, the probability of the state of nature that favors alternative B occurring is 0.30, and the probability of the state of nature that favors neither location A nor location B occurring is 0.20?
o Alternative A
o Alternative B
o Alternative A and B
o Neither Alternative A nor Alternative B
21. A consulting firm has contacted your company claiming that their analysis conclusively indicates that the probability of the state of nature that favors location A occurring is 0.50, the probability of the state of nature that favors location B occurring is 0.30, and the probability of the state of nature that favors neither location A nor location B occurring is 0.20. The consultants have offered to share their analysis with your company for a fee of $25.0 million. What is the Expected Value of Perfect Information in this scenario?
o $27,200,000
o $8,100,000
o $19,500,000
o $0
22. Should your company accept the consultant’s offer?
o Yes
o No
For questions 23 through 25, use the following payoff matrix data to create a sensitivity analysis data table that summarizes the expected monetary value for each possible alternative relative to the probability of the state of nature that occurs favoring Alternative A being varied from 0.0 to 1.0 in increments of 0.01.
Payoff Matrix
Alternatives State of Nature 1 (Favors A) State of Nature 2 (Favors B)
A $105.0 ($5.0)
B ($25.0) $55.0
A and B $80.0 $50.0
Neither A nor B $0.0 $0.0
23. For what range of probability of the state of nature that favors alternative A occurring is selecting alternative A the optimal decision?
o 0.00 – 0.04
o 0.05 – 0.68
o 0.69 – 1.00
o No range
24. For what range of probability of the state of nature that favors alternative A occurring is selecting alternative B the optimal decision?
o 0.00 – 0.04
o 0.05 – 0.68
o 0.69 – 1.00
o No range
25. For what range of probability of the state of nature that favors alternative A occurring is selecting both alternatives A and B the optimal decision?
o 0.00 – 0.04
o 0.05 – 0.68
o 0.69 – 1.00
o No range