Scope And Rationale Of Facility Management Construction Essay

Scope And Rationale Of Facility Management Construction Essay This assignment has been written to practically understand the functionality of facilities management within the context of pre-school nurseries. The role, scope and rationale of facility management in the Pre-school nurseries and benefits of outsourcing of different supporting functions in pre-school nurseries and advantages of services provided through outsource companies have also been explained through this activity. Suitable performance measures to improve the performance of facilities management services within the organization, encouraging health and safety environment and discussion of issues related to corporate social responsibility and dialogue on formulating effective facilities management strategy have also been included in this assignment. This activity has bestowed the researcher with practical understanding and knowledge of facilities management in business world. 2.1 Scope and Rationale of Facility Management in nurseries Brooks (2009) stated that Pre-School Nurseries are highly customized and valuable source of educating and training the children where not only core functions but supporting functions should also be managed appropriately. These supporting functions of any pre-nursery are managed by the facility managers. Facility management function is very important for given nurseries in the case study as core function of a nursery is to develop the skills and competencies of the children but supporting functions including pick and drop services, meal for the children, managing part time staff requirements, taking care of the internal environment of the nurseries and meeting health and safety requirements of any business. Atkin (2009) highlighted that facility Management is an interdisciplinary function of any organization as deep understanding and knowledge of core functions of any business, legal requirements for interior decoration in any business along with health and safety requirements in orde r to manage the facilities of any business are required to manage this section of the business. In case of pre-school nurseries the scope of facility Management is even more composite and complex as there need an increased understanding about the health and safety requirements inside and outside the organization as children are provided with the meal which should be hygienically approved and well standard. The condition of food when received from the suppliers should be well checked and preserved in hygienically approved place. In addition to this, school premises should be well preserved and taken care and should be decorated according to the psychological needs of the children and which is not possible without active participation and coordination of facility manager and teachers in the nurseries. In addition to this, fire exist should be effortless and simple and that is not even possible without the active participation of different departments in the nurseries. Hence range or e xtent of facility management in pre-school nurseries can cover every department in the nursery as training or teaching children is not enough but teaching children by taking care of health and safety, food hygienic issues to provide meals to the children, safe and clean pick and drop services to the children and interior decoration are the key areas of maintaining the service standards in nurseries. 2.2 Benefits of outsourcing and external provision of services Barrett (2003) stated that core or primary function of a pre-school nursery is to facilitate the learning and development of the children through stimulating and rich environment where there skills for the future are analyzed and developed. Nurseries are there to develop little scholars in the societies with the primary function of teaching and educating the children. This core function is most probably cannot be outsourced but there are still many supporting functions in the nurseries which can be outsourced and there are various benefits of outsourcing those functions. Maintaining safety for the children in the different nurseries CCTV can be fixed within and outside the nurseries on suitable positions in order to save those cameras and to have clear and complete view of the areas inside and outside the premises of the nurseries. CCTV is not a one time service as it need to be checked and sometime repaired with the passage of time and some special and technical skills and expertise are required to manage and repair such machines and a professional and authentic organization which has been licensed by the Government should be appointed for this purpose in order to have superior quality and guarantee sight of any incident and in order to have long lasting results from any CCTV machine. Moreover, pick and drop service for the children can only be managed through those service providers who have expertise in this field as taking care of the safety issues and timely reaching at different locations along with maintaining health, comfort and hygienic standards even within the coaches. A facility manager can ensure the health requirements and safety requirements through contracting with those service providers which have fixed CCTV in their coaches and can maintain the comfort standards by arranging comfortable and well designed seats inside the coaches. In addition to this, in five nurseries meal services for the children are also outsourced and being the facility m anager I would be responsible to take care of the needs of the children in order to provide them with their customized food and would also take care of the safety and hygiene standards of the suppliers along with ensuring safe and hygienically clean delivery of the food items till the premises of the nurseries where those food items would be stored according to their physical requirements. The teaching services are also some time outsourced by these five nurseries where part time teachers are gained through different agencies. Being the facility manager of these five nurseries I would consult teaching job specifications with the academic head in order to minutely understand the characteristics of relevant person for temporary hiring. I would contact with some agencies and select most appropriate which can provide us with relevant staff to fulfill our temporary gap. Being the facility manager of these five nurseries I would ensure the understanding level of the staff by arranging ini tial introductory induction plan with the academic head so that any gap in the understanding of newly hired staff can be minimized. All these outsourced services have several benefits as these are the specialized services which should be provided through specialized institutions as it becomes very difficult and sometime impossible to provide all these services on its own by the nurseries. Hence outsourcing becomes very beneficial and cost effective in order to have specialized and quality services through these external organizations. Nurseries cannot be so perfect in different supporting functions especially while dealing with children which is very much sensitive and can raise certain additional issues so contracting with external service providers is very much beneficial in many ways. 2.3 Introduction of suitable performance measures Developing the performance standards is very important to ensure safe and effective internal working of the nurseries. Booty (2009) stated that defining and grasping rules and policies is one aspect of enhancing performance of the staff but actual problems occur during implementation of those rules and polices in the organization where managing and improving performance of the employees really matters. He also added that quality in Nurseries services can be achieved through delivering motivation to the staff and employees on regular basis and acknowledging the importance and existence of the staff in delivering and maintaining the safe and healthy environment and services to the children with hazardless regularity and consistency. The hazards inside the building should be minimized by appointing staff members on those locations inside the organizational premises discouraging those behaviours which make students move towards such locations. This group of nurseries can also manage an u nannounced visit by Quality Assurer person in order to check the duties include in facility management functions in the organization. This would result in keeping a continuous check on the staff where they would take care of the health and safety and different similar issues in the nurseries. There should be points given on each visit by Quality Assurer and employees should be held accountable for decrease and increase in points based on horizontal and vertical analysis. Horizontal analysis would be based on comparing the performances of different nurseries and vertical analysis would be based on comparing performances of different visits in the same nursery at different periods of time. The staff performances should also be monitored and controlled through communicating and briefing with the staff on regular basis where any improvement in implanting and maintaining different facilities management issues should be discussed. Booty (2009) explained that designing and formulating stra tegies for facilities management needs multifunctional skills and competencies so managing performances during implementation of those policies also need well clear performance appraisal system. In addition to this its implementation also needs training and development which should also be given to improve the performances of the employees. 2.4 Issues related to corporate social responsibilities Baldry (2003) indicated that Organizational Facility Management commits to enhance the shareholders value in a socially responsible and ethical manner by taking care of the interests of stakeholders including suppliers, investors, customers, employees and local communities. Organizational Facility Manager should look for new services methods and product innovations that support the people living in it. The role of CSR (corporate social responsibilities) cannot be denied. In any business Facility managers are involved in formulation of such CSR reports as they are responsible to deliver sustainable performances throughout the year. This performance includes purchasing and waste management, staff management, health and safety management, organizational layout management and hazards management in case of nurseries business. Secondly, in case of nurseries facility managers will be involved in collecting and assembling information on organizational facilities in both social and environmen tal performance sections of corporate social responsibilities report. This report can only be successfully prepared if these organizational facilities in nurseries deliver sustainable performances and Facility managers have documented and tracked those performances so that data is readily obtainable and available. Nurseries waste management issues, quality of the suppliers and outsourcing companies, maintenance of health and safety issues along with noting different incidents and accidents in official records; all these are described and mentioned in corporate social responsibility report and facility managers are most relevant persons to manage all these functions in the organization. These issues can only be rightly tackled, supported and managed if nurseries have all these issues stored in black and white along with actions taken on different issues and remedies of those issues by the senior management. An increased level of transparency both for general readers and shareholders can only be enhanced through openness and clarity in CSR report where organizational facility manager plays a vital role in formulating that report. 2.5 Implications of health and safety legislations for Nurseries Laser (2004) stated that polices drawn by all these nurseries should be fully complied with European Community Law, the Health and Safety at Work Act 1974. Facility manager is responsible for health and safety matters concerning the premises of the nurseries and is also responsible to provide safe environment to children at nurseries. In addition to this, entire staff should be well aware of the potential hazards in and out of the nurseries premises and should actively protect children from those hazards. The staff should be given first aid training to support this process of safety. Facility manager is also responsible to record any accident and any incident in the Accident Report Book. These accidents should be informed to the parents as early as possible. All staff should be well aware of transmission of the infection from one body to the other body. Kaiser (2006) summarized few elements to be taken care for effective management of organizational facilities with respect to health and safety requirements. A facility manger should provide healthy and safe atmosphere to the children. A facility manager should be responsible to achieve highest standards of occupational hygiene, welfare, safety and health. A facility manager is also responsible to prevent ill-health, injuries, accidents and other minor incidents by identifying and eliminating hazardous situations inside the nurseries premises. A facility manager should also motivate and involve staff in different matters regarding Health and Safety of the staff in the organization. A facility manager should also control all those situations which may prove hazardous to the health and safety in the nurseries and which result in causing damage to individuals and equipments in the organization. A facility manager should also take care of the airy environment and ventilation of the nursery premises in order to avoid any suffocation and order to ensure healthy environment. 2.6 Selection of strategy for effective facility management Huston (2009) indicated that a robust strategy for the effective and efficient management of the facilities of an organization can only be developed if it is within the context of organizational business plan and space strategy. It should involve strategic plan and objectives for managing facilities in any organization. A strategy of organization facility management should contain following aspects. Alan (2007) stated that facility management strategy of nurseries should consider the future needs of the nurseries by differentiating between core and non core business activities of the nurseries. This strategy should assist the nurseries in effectively managing its processes and functions in order to meet those needs of the nurseries. Huston (2009) elaborated that this strategy should develop appropriate, efficient and quality resources to meet different needs of nurseries and should also draw a line between using internal resources and obtaining external help to meet needs; for instance there must be coordination between different functions of the nurseries as introducing different new toys and games for the children must be consulted with facility managers to assess either internal environment and premises is suitable for these types of games to be brought in the nurseries or either some major or minor changes are required to improve the suitability of those toys and games with organization layout and space issues. Tuveson (2008) stated that this strategy should also ensure that finances gained are spent economically to earn maximum benefits for the business. In addition to this, this strategy should also establish a budget to cover the short term needs and to generate best value for long term. This strategy should confess the importance of information technology in order to effectively manage and control nurseries facilities management. The workable strategy of facilities management in the organization can be divided into three stages including top level analysis, analyzing requirements, developing and implementing solutions by putting different plans to work. Thorough understanding and review of the different nurseries would help the facility manager in assembling the most important material facts for designing effective facilities management strategy. Nurseries needs include managing healthy and safety within the premises, ensuring hygienic standards, managing appropriate teachers, managing regularity and consistency in children and staff for proper functionality of its business, encouraging safe environment by effectively handling hazardous places inside the premises, utilizing organizational space appropriately, managing layout issues and constructing such layout for games and different activities which are creative, innovative but not dangerous, managing well secured, safe, clean and timely pick and drop services and managing food quality and ensuring health and safety standards in all the possible ways. These needs should be well understood by a facility manager so that space utilization strategy, health and safety strategy and outsourcing strategy can be effectively managed. In addition to this broad picture of resources, systems and processes can be taken through effective need analysis where cost analysis would also help in formulating efficient budgets for facility manager. This stage would help in assembling information about organizational needs for facilities management which later on needs interpretation and explanation for the adoption of information. In adoption stage the clear discussion and interpretation of information would result in allowing innovative and new ideas through brain storming process. Generating different options for actually implementing that information to meet the organizational needs for facility management. Developing criteria for judging all those options which are presented by different participants. Evaluating those options on the set criteria for judging those options. Most preferred option is selected through these stages in order to select most appropriate facilities management strategy of the nurseries. One selected option is then implemented into the nurseries setup and feedback is given on the selected options where further improvement is made through gradual processing of organizational tasks and duties. 3.1 Conclusion If nurseries buildings and different other facilities are not properly and rightly managed they may start impacting on nurseries performance as facilities and building in the organizations (nurseries) have great potential and scope to increase performance when optimal use of their space is made and supportive environment for business and service is created. No universal approach can be designed to manage organizational facilities as every organization has its own specific needs even within the same industry or business sector and same goes to nursery business. The best value to the nurseries can only be provided if facility manager rightly understands those specific needs. Moreover, organizational facility management strategy should be corner stone of its accommodation strategy and should not adjunct to it. Before choosing a most relevant solution, a facility manager should consider the cost incurred in both cases while providing those facilities through outsourcing or in-house. This complete picture would assist facility manager in deciding the most appropriate solution on best value grounds. Effective facilities management strategy can only be developed through integrated and long term service provision.

Mktg 301

7) Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Number of sales people working| Sales (in $1000)| 4| 12| 5| 13| 8| 15| 10| 16| 12| 20| 12| 22| 14| 22| 16| 25| 18| 25| 20| 28| x=11. 9| y=19. 8| SD(x)=5. 30| SD(y)=5. 53| a) Find the slope estimate, b1. Use technology or the formula below to find the slope. b1=rsysx Enter x,y Data in TI-84 under STAT > STAT > CALC > 8: LinReg(a+bx) b1=1. 023 b) What does b1 mean, in this context?The slope tells how the response variable hanges for a one unit step in the predictor Thus, an additional; $1,023 of sales associated with each additional sales person working. c) Find the intercept, b0. b0=y-b1x =19. 8-1. 023(11. 9) For this problem, use technology, rounding to three decimal places. b0=7. 622 d) What does b0 mean in this contet? Is it meanful? The intercept serves as a starting value for the predicitons. It shuld only be interpreted if a 0 value for the predictor variable makes sense for the context of the situation. On average, $7,622 is expected when 0 sales people are working.It is not meaningful because it does not make sense in this context. e) Write the equation that predicts Sales from Number of Sales People Working. Recall that the slope of the equation b1=1. 023 and the intercept is b0=7. 622 Complete the equation. Sales=7. 622+1. 023 *(Number of Sales People Working) f) If 19 people are working, what sales do you predict? Substitute 19 for the number of sales people working in the equation found in the previous step and solve for Sales. Sales=7. 622+1. 023 *(Number of Sales People Working) =7. 622+1. 023*19Substitute. =27. 059Simplify. *Note that each unit of Sales represents $1000. Thus, the predicted sales for 19 people working is 27,059 dollars. g) If sales are actually $26,000, what is the value of the residual? Subtract the predicated value found in the previous step from the actual value. 26,000-27,059=-1059 Thus, t he value of the residual is -1059 dollars. h) Have the sale been overestimated or underestimated The predicted sales are $27,059 and the actual sales are $26,000. Since $27,059 > $26,000, the sales were overestimated. 13) Of the 46 individuals who responded, 25 are concerned, and 21 are not concerned. of those concerned about security are male and 5 of those not concerned are male. If a respondent is selected at random, find each of the fallowing conditional probabilities. | Male| Female| Total| Concerned| 9| 16| 25| Not Concerned| 5| 16| 21| Total| 14| 32| 46| a) The respondent is male, given that the respondent is not concerned about security. P(Male|Not Concerned) = 521 = 0. 238 b) The respondent is not concerned about security, given that is female P(Not Concered|Female) = 1632 = 0. 500 c) The respondent is female, given that the respondent is concerned about security. P(Female|Concerned) = 1625 = 0. 40 14) It was found that 76% of the population were infected with a virus, 21% were without clean water, and 18% were infected and without clean water | Clean Water| | | Yes| No| Total| Infected| 0. 58| 0. 18| 0. 76| Not Infected| 0. 21| 0. 03| 0. 24| Total| 0. 79| 0. 21| 1. 00| a) What’s the probability that a surveyed person had clean water and was not infected? .21 had clean water and was not infected 15) A survey concluded that 54. 4% of the households in a particular country have both a landline and a cell phone, 32. 6% have only cell phone services but no landline, and 4. 6% have no telephone services at all. ) What proportion of households have a landline? Begin by making a contingency table. | Cell Phone| | | Yes| No| Total| Landline| 0. 545| 0. 083| 0. 628| No Landline| 0. 326| 0. 046| 0. 372| Total| 0. 871| 0. 129| 1. 00| The completed contingency tables shows that P(landline) = 0. 628. b) Are having a cell phone and having a landline independent? Explain. Events A and B are independent when P(B|A) = P(B). To determine wheter having a cell pho ne and having a landline are indepented, find P(landline|cell phone) and P(landline). Recall from part a) that P(landline) =0. 628 PBA=P(A and B)P(A)Use the formula to find P(landline|cell phone) Plandlinecell phone=P(landline and cell phone)P(cell phone) Since the contingency table shows that P(landline and cell phone)=0. 545 and P(cell phone)=0. 871, substitute these values into the equation. Divide to find the conditional probability, rounding to three decimal places. Plandlinecell phone=0. 5450. 871=0. 626 Thus, P(landline|cell phone)=0. 626 and P(landline)=0. 628. Because 0. 626 is very close to 0. 628, having a cell phone and having a landline are probably independent. Of the households surveyed, 62. 6% with cell phones had landlines, and 62. 8% of all households did. 6) A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 30% of potential customers will choose the Day Plan, which does not include overnight ac commodations; 30% will choose the Overnight Plan, which includes one night at the resort; and 40% will choose the Weekend Plan, which includes two nights. a) Find the expected value of the number of nights that potential customers will need Vacation Package| Nights Included| Probability P(X=x)| | Day Plan| 0| 30100=0. 3| | Overnight Plan| 1| 30100=0. 3| | Weekend Plan| 2| 40100=0. 4| | This, P(X=0)=0. 3, P(X=1) =0. 3, and P(X=2)=0. Use the formula E(X) = ? x †¢ P(x) to detrime the expected value. E(X) = ? x †¢ P(x) = 0(0. 3) +1(0. 3) +2(0. 4) = 1. 1 There, the expected value of the number of night potential customers will need is 1. 1 b) Find the standard deviation of the number of nights potential customers will need. The standard deviation is the square root of the variance. First, Find the Variance: To do so, find the deviation of each value of X from the mean and square each deviation. The variance is the expected value of these squared deviations and is found using th e formula below. = Var(X) = ? (x –  µ)? P(x) Find the deviation for each value of X.Remember that E(x)=1. 1 Vacation Package| Nights Included| Probability P(X=x)| Deviation (x – E(X))| Day Plan| 0| 30100=0. 3| 0 – 1. 1 = -1. 1| Overnight Plan| 1| 30100=0. 3| 1 – 1. 1 = -0. 1| Weekend Plan| 2| 40100=0. 4| 2 – 1. 1 = 0. 9| Now find the variance using the formula =Var(X)=? (x –  µ)? P(x) Var(X) = ? (x –  µ)? P(x) = (-1. 1)? (0. 3) + (-0. 1)? (0. 3) + (0. 9)? (0. 4) = 0. 69 Finally, the standard deviation also known as ? is the square root of the variance. ? = Var(x) = 0. 69 = 0. 83 Therefore, the standard deviation of the number of nights potential customers will need is approximately 0. 83 nights. 7) A grocery supplier believes that in a dozen eggs, the mean number of broken eggs is 0. 2 with a standard deviation of 0. 1 eggs. You buy 3 dozen eggs without checking them. a) How many broken eggs do you get? The expected value of t he sum of random variables is the sum of the expected values of each idividula random variable. Find the sum of the expected values where X is the total number of broken eggs in the three dozen, and X, X, X Represent the three individual dozen eggs. E(X) = E(X1) + EX2+ EX3 = 0. 2 + 0. 2 + 0. 2 = 0. 6 Therefore, the expected value of X is 0. 6 eggs. b) What’s the standard deviation?The variance of the sum of independent variables is the sum of their individual variances. Find the variance for each carton, add the variances, and then take the square root of the sum to find the standard deviation. The variance of each individual dozen is the square of each dozens standard deviation. Var(X1) = Var(X2) = Var(X3) = 0. 12= 0. 01 Find the sum of the variances to find the variance of the sum. Var(X) = VarX1+ VarX2+ VarX3 = 0. 01 + 0. 01 + 0. 01 = 0. 03 Recall that the standard deviation is the square root of the variance. Find the standard deviation. SD(X) = Var(x) = 0. 03 = 0. 17Ther efore, the standard deviation is 0. 17 eggs c) What assumptions did you have to make about the eggs in order to answer this question? The variance for the sum of random variables is only the sun of variances of each random variable in certain cases. Review the assumption that must be made to allow the variance to be the sum of the individual variances. 18) An insurance company estimates that it should make an annual profit of $260 on each homeowner’s policy written, with a standard deviation of $6000. a) Why is the standard deviation so large? Home insurance is used to protect the owner financially in the event of a problem.If a catastrophe occurs, then the insurance company will cover the cost of the damage. If a catastrophe never occurs, then the insurance company pays nothing. Meanwhile, the owner pays the insurance company at regular intervals whether or not a catastrophe occurs. The expected value is the mean annual profit on all of the policies and the standard deviatio n is a measure of how much annual profits can differ from the mean. Use this information with the fact that claims are rare, but very costly, occurrences. b) If the company writes only four of these policies, what are the mean and standard deviation of the annual profit?LetX1,X2, X3,†¦,Xn represent the annual profit on the n policies and let X be the random variable for the total annual profit on n polices written. X=X1+X2+ X3+†¦+Xn The expected value of the sum is the sum of the expected values. Find the expected value of the annual profit on each policy. EX1=EX2=EX3=EX4=$260 Now find the sum of the expected values. EX=EX1+EX2+EX3+EX4 =260+260+260+260 = $1040 Therefore, the mean annual profit is $1040 To find the standard deviation of the annual profit, use the fact that te variances of the sum of independent variables is the sum of their individual variances. First find the variance for each policy.The variance for the policy is the square of the standard deviation. VarX 1=VarX2=VarX3=VarX4=60002=36,000,000 VarX=VarX1+VarX2+VarX3+VarX4 = 4(36,000,000) = 144,000,000 Evaluate the square root of the variance to find the standard deviation. SDX=VarX =144,000,000 =$12,000 Therefore, the standard deviation is $12,000 c) If the company writes 10,000 of these policies, what are the mean and standard deviation of annual profit? The expected value of the sum is the sum of the expected values. The expected value of each policy was found earlier. EX1=EX2=EX3=†¦ =EX10,000=$260 Now find the sum of expected values. EX=EX1+EX2+EX3+†¦ +EX10,000 10,000(260) =$2,600,000 Therefore, the mean annual profit is $2,600,000 To find the standard deviation of the annual profit, use the fact that the variance of the sum of independent variables is the sum of their individual variances. First find the variance for each policy. The variance for the policy is the square of the standard deviation and was found earlier. VarX1=VarX2=VarX3= †¦ =VarX10,000=36,000,000 Now sum the variances to find the variances of the sum. VarX=VarX1+VarX2+VarX3+†¦ +VarX10,000 =10,000(36,000,000) =360,000,000,000 Evaluate the square root of the variance to find the standard deviation. SDX=Var(X) =360,000,000,000 $600,000 Therefore, the standard deviation is $600,000. d) Do you think the company is likely to be profitable? Recall that the mean annual profit for 10,000 policies is $2,600,000. While this number seems quite large, it is necessary to determine how likely a profit is to ensure that this company will be profitable. Find the distance in standard deviation of $0 from the mean to determine how rare an occurrence of no profit would be. z=x- =0-2,600,000600,000 =-4. 3 Thus, $0 is 4. 3 standard deviation below the mean. **Note that approximately 95% of the annual profits should lie within two standard deviations of the mean.Evaluate whether the distance of $0 from the mean is convincing enough to determine whether or not the company will be profitable. e) W hat assumptions underlie your analysis? Can you think of circumstances under which those assumptions might be violated? The variance of the sum of random variables is only the sum of the variances of each random variables in certain cases. Review the assumption that must be made to allow the variance to be the sum of the individual variances. Then chose the situation that would create an association among policy losses. 19) A farmer has 130 lbs. of apples and 60 lbs. f potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0. 8 dollars and a standard deviation of 0. 4 dollars. Similarly, for a pound of potatoes, the mean price is 0. 4 dollars and the standard deviation is 0. 2 dollars. It also costs him 5 dollars to bring all the apples and potato’s to the market. The market is busy with shoppers, so assume that he’ll be able to sell all of each type of produce at the day’s price. a) Define your random variables, and use them to express the farmer’s net income. A random variable’s outcome is bases on a random event.Therefore let the random variables represent the factors that will be randomly determined each day. The random variables should represent the market prices of the two items. A = price per pound of apples P = price per pound of potatoes The profit is equal to the total income minus the total cost. The income is found by multiplying the market price for apples by the total number of pounds sold and adding it to the product of the market price for potatoes and the number of pounds of potatoes sold. The total cost is the transparent cost. Profit = 130A + 60P – 5 b) Find the mean. The mean of the net income is the expected value of the profit.Profit = 130A + 60P – 5 E(Proft) = E(130A + 60P – 5) Use the property E(X + Y) = E(X) + E(Y) to express the expected value of the profit as the sum of two separate expected values E=(Profit) = E(130A +60P -5) = E [(130A) + (60P – 5)] = E(130A) + E(60P – 5) Now use the property EX ±c= E(X) ±c E(Profit) = E(130A) + E(60P – 5) = E(130A) + E(60P) – 5 Finally, use the property E(aX) = aE(X) to remove the coefficient from the expected values. E(Profit) = E(130A) + E(60P) – 5 = 130E(A) + 60E(P) – 5 Substitute the known expected values of the prices of apples and potatoes in the equation. E(Profit) = E(130A) + E(60P) – 5 E(0. 8) + E(0. 4) – 5 Evaluate the expected profit. E(Profit) = 130(0. 8) + 60(0. 4) – 5 = 123 Therefore, the mean is 123 dollars. c) Find the standard deviation of the net income. To find the standard deviation, first find the variance and then take the square root, since the properties useful in this case are in terms of variance and not standard deviation SD(Profit) = Var(Profit) = Var(130A+60P-5) First use the property Var(X + Y) = Var(X) + Var(Y) to express the variance of the profit as the sum of two separate v ariance Var(Profit) = Var(130A + 60P – 5) = Var[(130A) + (60P – 5)] =Var(130A) + Var(60P – 5)Now use the property Var(X  ± c) = Var(X) to simplify the second variance Vr(Profit) = Var(130A) + Var(60P – 5) = Var(130A) + Var(60P) Finally, use the property VaraX=a2VarX to restate each variance. Var(Profit) = Var(130A) + Var(60P) = 1302VarA+ 602VarP = 16,900Var(A) + 3600Var(P) Evaluate the variance of the profit. Var(Profit) = 16,900(0. 16) + 3600(0. 04) = 2848 Lastly, find the standard deviation, rounding to two decimal place. SD(Profit) = VarProfit = 2848 = 53. 37 Therefore, the standard deviation of the net income is 53. 37 dollars. d) Do you need to make any assumptions in calculating the mean?Recall that the mean of the sum of two or more random variables is the sum of the means. Determine what, if any, assumptions are made to use this property. Do you need to make any assumptions in calculating the standard deviation? Recall that the variance of the s um of two random variables is only the sum of their individual variances in certain cases, Determine what, if any, assumptions are made to use this property. 20) A salesman normally makes a sale (closes) on 65% of his presentations. Assuming the presentations are independent, find the probability of the following. ) He fails to close for the first time on his sixth attempt. Use the formula below to determine the probability, where p is the probability success, q=1 – p and X is the number of trails until the first success occurs. P(X=x) = qx-1p Find the values for p and q. **Note that in this case that a success is defined as failed to close p = 0. 35 q = 0. 65 Substitute and solve to find P(X=6). Rounding to four decimal places P(X=6) = qx-1p = 0. 656-1(0. 35) = 0. 0406 Therefore, the probability he fails to close for the first tie on his sixth attempt is 0. 0406 b) He closes his first presentation on his fifth attempt.Find the values for p and q. **Note that in this case tha t a success is defined as making a sale p = 0. 65 q = 0. 35 Substitute and solve to find P(X = 5), rounding to four decimal places P(X=5) = qx-1p = 0. 355-1(0. 65) = 0. 0098 Therefore, the probability he closes his first presentation on his fifth attempt is 0. 0098 c) The first presentation he closes will be on his second attempt. Find the values for p and q. Note that in this case that a success is defined as making a sale. p = 0. 65 q = 0. 35 Substitute and solve to find P(X=2) P(X=2) = qx-1p = 0. 352-1(0. 65) = 0. 2275Therefore, the probability the first presentation he closes will be on his second attempt is 0. 2275 d) The first presentation he closes will be on one of his first three attempts. Use the fact that the compliment of an even is equal to 1 – P(X=x) to find the probability. The compliment event is that he will not close a sale on any of his first three attempts. Find the probability that he does not close on his first three attempts, rounding to four decimal pl aces. 0. 353=0. 0429 Subtract from 1 to find the probability the first presentation he closes will be on one of his first three attempts 1 – 0. 429 = 0. 9571 Therefore, the probability the first presentation he closes will be on one of his first three attempts is 0. 9571 21) College students are a major target for advertisements for credit cards. At a university, 73% of students surveyed said that they had opened a new credit card account within the past year. If that percentage is accurate, how many students would you expect to survey before finding one who had not opened a new account in the past year? First check to see that the cells are Bernoulli trials. Trials are Bernoulli if the following three conditions are satisfied. 1.There are only two possible outcomes (called success and failure) for each trial. 2. The probability of success, denoted p, is the same on every trial. (The probability of failure, 1 – p is often denoted q. ) 3. The trials are independent Ther e are only two possible outcomes for each trial because a student either opened a credit card account in the past year or they did not. The probability of success is the same on every trial, based on the percent given in the problem statement. The trails are independent because each student’s response is not dependent on any other student’s response.Thus, the trials of surveying the students are Bernoulli trials. A geometric probability model models how long it will take to achieve the first success in a series of Bernoulli trials. Let X be the number of students that will have to be surveyed before finding the first student who did not open a credit card in the past year. The two outcomes are a student who did not open a credit card account in the past year *success) and a student who opened a credit card account in the past year (failure). The probability of a failure is given in the problem statement as q = 73% = 0. 73.Find the probability of success by subtracting this from 1. P = 1 – 0. 73 = 0. 27 Find the expected value of X. In a geometric model, the expected value is EX= 1p , where p is the probability of success. Round up to the nearest integer. EX=10. 27=4 Therefore, on average, you would expect to survey 4 students before finding one who had not opened a new account in the past year. 22) A certain tennis player makes a successful first serve 82% of the time/ Assume that each serve is independent of the others. If she serves 7 times, what’s the probability she gets a) all 7 serves in? b) exactly 5 serves in? ) at least 5 serves in? d) no more than 5 serves in? The first step is to check to see that these are Bernoulli trails. The first serves can be considered Bernoulli trials. There are only two possible outcomes, successful and unsuccessful. The probability of any first serve being good is given as p = 0. 82. Finally, it is assumed that each serve is independent of the others. Next define the random variable. Each questi on deals with the number of serves, so let X be the number of successful serves in n = 7 first serves. Now determine which probability model is appropriate for these problems.Recall that geometric probability models deal with how long it will take to achieve a success. A binomial probability model describes the number of successes in a specific number of trails. All the question deal with the number of successful serves so the binomial probability model Binom(7,0. 82 is appropriate here. a) all 7 serves in? The probability that she ges all 7 serves in is P(X=7). To use the binomial probability model Binom(n,p), use the fallowing formula, where n is the number of trials, p is the probability of success, q is the probability of failure (q = 1 – p), and X is the number of successes in n trials.PX=x= nxpxqn – x, where nx= n! x! n-x! First substitute the correct values into the formula PX=7= 770. 8270. 187- 7 Now simplify. P(X = 7) ? 0. 249 Therefore, the probability that s he gets all 7 serves in is approximately 0. 249 binomPDF(7, . 82, 7) = b) exactly 5 serves in? The probability she gets exactly 5 serves in is P(X = 5). As in part a, use the formula PX=x= nxpxqn – x to find this probability PX=5= 750. 8250. 187 – 5 ?0. 252 Therefore, the probability she gets exactly 5 serves in is approximately 0. 252 binomPDF(7, . 82, 5) = c) at least 5 serves in?To find P(at least 5 serves in), first determine and an expression that is equal to this probability. Note that the wording â€Å"at least 5†, means 5 or more, meaning that there can 5, 6, or 7 serves in. Thus, the probability equals P(X=5) + P(X=6) + P(X=7). So to find the probability that she got at least 5 serves in, evaluate. P(X=5) + P(X=6) + P(X=7) = 75(0. 82)50. 187-5+76(0. 82)6(0. 18)7-6+77(0. 82)7(0. 18)7-7 ?0. 885 Therefore, the probability she gets at least 5 serves in is approximately 0. 885 binomPDF(7, . 82, 5) + binomPDF(7, . 82, 6) + binomPDF(7, . 82, 7) = d) no more th an 5 serves in?To find P(no more than 5), first determine an expression that is equal to this probability. Note that the wondering â€Å"no more than 5† means 5 or less, meaning that there can be 0 thru 5 successful serves. Thus, the probability equals P(X? 5). So to find the probability that there are no more than 5 serves in, evaluate P(X? 5), which is equal to P(X=0) + P(X=1) + †¦ + P(X=5), using the formula PX=x= nxpxqn – x P(X=0) + P(X=1) + †¦ + P(X=5) = 70(0. 82)00. 187-0+71(0. 82)1(0. 18)7-1 + †¦ + 75(0. 82)5(0. 18)7-5 ? 0. 368 Therefore, the probability that there are no more than 5 serves in is approximately 0. 368 binomCDF(7, . 82, 5)

Finding Freedom: What it is and what it’s not Essay

Abstract Human freedom could very well be the most controversial topic in our society. To some, human freedom is the freedom to be educated, to work and provide financially for yourself and your family. The freedom to drive a motor vehicle. To vote for the president you truly believe in. To move about freely from one city, state, country or continent to another. In this report, I will investigate the perceived legitimacy of these freedoms, amongst others, and expose the variations in the definition of this word â€Å"freedom.† Finding freedom Many aspects of life come to mind when one is brought the question, â€Å"are you free?† The average person would say yes, they are. But, what does free actually mean? Most would say the ability to choose from any option dictating their personal future. But, there is a contingency to every decision we make and every freedom or option we have. We all want to make our own choices and decide which direction we want our life to go in, but that comes with a price. That price could very likely be one that we may not be willing to pay. Is that actually freedom? In order to take advantage of the freedom to drive an automobile, you must first pass a written test. Following the written test, you are required to pass a road test and pay the fees to become a licensed driver. Not to mention that you must have current insurance to even drive a vehicle after you’ve done all these things. With that said, you have the freedom to operate a motor vehicle, but you don’t have the fre edom to do so without first successfully completing the aforementioned steps. The United States boasts the fact that all of its citizens have the freedom to travel freely, both within and outside of its borders. Of course there is a contingency. They must know where you are going and for how long as well as other information one probably wouldn’t offer it that were not required to exercise their â€Å"freedom.† Describing human freedom is problematic at best as most see simply as the ability to do what you want. Jerry A. Coyne (2012) Stated that while people do have the ability to do what they want, what they want is predetermined by laws just like the laws of physics. In that sense, our so-called freedom is already within certain boundaries. Not realizing this, it’s even harder to understand that we already exercise our freedom within boundaries of the natural boundaries that have already existed. Finding freedom The idea of human freedom fits into the field of sociology though the fact that ones personal idea of being free directly results in the decisions that person makes. The collective decisions of a society shape a society. The degree of freedom one feels varies from person to person, but however free they feel actually indirectly shapes their society. Understanding this concept can grant invaluable insight on the dynamics of a society and their patterns of behavior. James M. Buchanan (1975) suggested that social stability requires an agreement on and enforcement of a structure of individual rights, meaning that in a society there is a general consensus that they all have the freedom to act in tolerable ways and make certain decisions. This also promotes the idea that there are still boundaries to the freedom we perceive and fight to keep. It’s fairly obvious at this point that freedom is not exactly what most would think it is and that the term is often confused with free will. John Locke (1997) believed that free will was the ability to override instinct. For instance, if one is hungry and they chooses not to eat to do something else, they have exercised their free will. But with true freedom, one would be able to choose not to eat at all. We know that we have freedom of speech and press and all of the other amendment, but they were given to us. True freedom has no proposal and enactment date. You either have it or you don’t. The fact is that the conundrum called freedom is actually not freedom at all. In James M. Buchanan’s (1975) study of commonality and non-economic interaction, he stated that freedom as a norm or rule for social intercourse has little or no meaning until or unless individuals are first identified in terms of acknowledged limits of behavior. With that said, if we all carried on with no interaction and did what ever we wanted to, that would be as close as we could ever get to freedom. Within a society, culture or family setting, there will always be a behavioral boundary. While we have the free will to make decisions within those boundaries, we do not have the freedom to make our own boundaries as long as we are a part of a society. Finding freedom Further research into the concept of human freedom, I believe, would offer a great deal of value to the field of sociology. One’s own sense of freedom plays a huge part in their day to day actions and what path they choose in their own life. Sociology, by definition, is the study of the development, structure and functioning of human society. The development of society is based on decisions made by those who lead the way of development and the citizens who decided elect them based on their own sense and concept of freedom. It is my understanding that the very foundation of a society is the peoples’ sense of freedom, collectively, and they make choices based on that sense of freedom. This could give insight into the research of crime, poverty and suicide rates as well as chronic depression and people who are withdrawn from society. Finding Freedom Discussion Though it may not be easy to grasp immediately, that our sense of freedom is what drives us, at this point it would be hard to object. Dr. Mark Cooray (1997) explained freedom is the liberty of the individual coupled with concern by the liberated individual for the liberties of others. In other words what we call freedom is merely a box that we are allowed to move about freely within. Only because our actions affect others and their sense of freedom do we have to operate within the confines of freedom. That leads me to believe that true freedom can only be achieved by on outside of a society or one happens to be an exception to the rule. It has been found that no one can truly be free without encroaching the freedom of another within their society. According the John Locke (1997) freedom is merely a better word for free will, when thought of literally, as there is no tangible concept of actually freedom. With that said, I can still conclude that people still do not feel as free as they actually are although still confined to the boundaries of freedom. This inference, I believe, could help with the research of several of societies ailments and perhaps empower some of those who may feel helpless and resort to deviant means. Finding Freedom References James M. Buchanan (1975). The Paradox of â€Å"Being Governed† – James M. Buchanan, The Collected Works of James M. Buchanan, vol. 7 (The Limits of Liberty: Between Anarchy and Leviathan) Jerry A. Coyne (2012). Why you really don’t have free will. USA Today John Locke (1997). What is human freedom?

To What Extent was the European ‘Scramble for Africa’...

The ‘scramble for Africa’ was a phenomenon in the world between the years 1880-1914. The ‘dark continent’ was relatively untouched by Europeans up until this point, with few ports of control on the coasts in the west, which were remnants of the slave trade, and in the south, Britain held the Cape, taken from the Dutch during the French Revolutionary Wars. So, during a period of 30 years, it came to pass that almost the whole of Africa was taken by Europeans. (Except Liberia a colony for freed American slaves, and Abyssinia managed to hold out against Italian aggression). It will be my objective in this essay to analyse the economic factors which resulted in the almost complete colonisation and takeover of Africa, and also to determine to†¦show more content†¦Thereafter thousands of British immigrated to South Africa to work in or control the mining industry. It could be said that the ‘history of twentieth-century southern Africa is to a very l arge extent dominated by the history of mining’ which to a certain extent is true. Most of the imperial expansion in South Africa at first glance does appear to have economic reasons. This can be further seen with Cecil Rhodes when he extended British influence to the northern reaches of South Africa in search for a second rand in which his whole expedition looks to be like conquistadores in search of land and gold . In 1910 the Transvaal republic was annexed by Britain, while economic reasons seem reasonable at first it can be argued that ‘political control of the Transvaal was not sought in order to control the gold-mines nor secure access to the supply of gold’ , that the British wanted to unify the region as part of the British Empire. Originally however, the importance of South Africa to the British was to protect the sea route to India, which was still vital, even after the Suez Canal was built, because the British were sure that they could defend the Cape with their naval strength, but were not so sure about the defence of the Suez if needed. Gallagher and Robinson assert that ‘Great Britain was in South Africa primarily to safeguard the routes to the east’ . However, this is still an economic factor. That Britain wanted to protect trade and strategy in the east, and whileShow MoreRelatedThe Impact Of Economics And Finance On Influencing Britain s Relationship With Its African Empire1917 Words   |  8 Pagessignificance of economics and finance in influencing Britain’s relationship with its African empire in the period c1870-c1981 Between 1870 to 1981, economic factors occurred throughout the 111 years. 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