Troy University Probability of Winning Specific Amounts of Cash Problem
The Governor for the State of Alabama is considering starting a weekly lottery to help raise money for the state. The Gove …
Troy University Probability of Winning Specific Amounts of Cash Problem
The Governor for the State of Alabama is considering starting a weekly lottery to help raise money for the state. The Governor’s buddies have devised a game where participants must pick six numbers from a set of possible winning numbers. The more winning numbers the participant picks correctly, the greater the prize. The cost to participants is $1 for each entry into the game. On the back of each ticket is the following information regarding the probability of winning specific amounts of cash. Numbers Matched Prize x Probability P(x) 1 $1 0.4130195 2 $10 0.132378 3 $100 0.0176504 4 $1,000 0.0009686 5 $10,000 0.0000184 6 $100,000 0.0000001 Note the following: The $1 fee to play the game is a sunk cost for the contestant. That is, regardless of how many, if any, numbers the contestant matches, the contestant does not get the $1 back. In the case of the contestant matching 2 numbers, the contestant pays $1 to play and wins $10, so the contestant’s net winnings are $9. The grand prize is fixed at $100,000, unlike other lotteries where the amount varies each week according to the number of contestants and winners during the previous week. Assume the probabilities provided above are accurate. Your cousin Louie tells you that he is going to buy one ticket every week, and he will have won almost $200 by the end of the year. Should the governor rethink the lottery? Do you have any suggestions for improving the lottery? Is Louie correct about pocketing approximately $200?
Review the Case Study bellow Next, examine the main structural and process changes that will be required to design and imp …
Review the Case Study bellow Next, examine the main structural and process changes that will be required to design and implement family-style dining at this facility. Suggest a plan of action to address Ms. Laird’s concerns from the Planning Committee meeting regarding noise, security, and other potential disruptions expected during the construction of the new kitchens and dining areas. Provide a rationale for your response.City Nursing Home (CNH) is a nonprofit, independent, 200-bed facility located outside a major city in the western United States. The community has a population of nearly 150,000 with a high rate of poverty. CNH has a current occupancy rate of 97%, which is significantly higher than the state and national averages. CNH is ranked highly on Medicare’s 19 quality indicators (Table CS7–1), but the facility had eight deficiencies cited on its certification survey when it was inspected about a year ago (Table CS7–2). The four-story building was opened 32 years ago and has maintained an excellent reputation for delivering high-quality patient care. Staff stability in a community that offers relatively few jobs has been one of the main factors that has contributed to the quality of care. The facility trains its own certified nursing assistants (CNAs). With less turnover compared with the industry, and having a pool of trained CNAs to fill vacancies, the facility maintains above-average staffing levels. The facility also takes pride in having its own in-house rehabilitation therapy staff. Ms. Morehouse has been the administrator of CNH for the past 12 years. For its current strategic plan, the governing board has approved adoption of culture change mainly through self-managed work teams in nursing services and the implementation of family-style dining. Implementation of this plan would require both structural and process changes. The existing kitchen is located in the basement of the building, and the main dining room is on the first floor. Using an elevator, food is transported in carts with hot and cold compartments. CNAs pick up the meal trays with preportioned food straight from the food carts, check the resident’s name against the meal card on each tray, and place the tray in front of the resident. Although the service is efficient, its appeal is very institutional. However, residents and families have been generally satisfied with the meals. One main issue in the past few years has been three leg injuries that the food service associates sustained while transporting the heavy carts. One of the injuries was serious enough to keep the associate away from work for 4 months. Shortly after returning to work, that associate resigned to take a job at the local McDonald’s. One year, the kitchen sustained some flooding after heavy spring rains and had to be closed down for almost 2 weeks. Food services were temporarily contracted out. Ms. Morehouse and the board worked together to engage the architectural firm of Caplin & Reese. The firm has had some experience with modern architectural designs for nursing homes. Considering the financial resources and other logistical issues, the facility would redesign its kitchen and dining areas in three to four phases. It is anticipated that over the next few years, each floor will have its own family-style kitchen and dining area. CNH is now in the early planning stage, having recently formed a Food Service Planning Committee. The Planning Committee met 2 weeks ago, and Ms. Morehouse is reviewing the minutes from that meeting: Minutes from the Planning Committee Meeting Present: Ms. Morehouse, administrator; Mr. Hassan, finance and admissions coordinator; Mr. Washington, food services director; Ms. Laird, director of nursing; Ms. Smith, rehabilitation supervisor; Mr. Keith, construction representative; Mr. Morgan, designer; Mr. Welbourne, contractor; Ms. Reese, architect. The meeting started at 9 a.m. Ms. Morehouse began with introductions of those present. She explained that culture change in the nursing home industry was going to gain momentum and, if traditional facilities did not adapt to changing consumer expectations, they would not be able to compete. Hence, the governing board had authorized a long-range plan to implement certain structure and process changes. Modification of current dining arrangements was part of this long-range plan. Ms. Morehouse then opened the meeting for comments and questions from those present. Mr. Washington, who has been employed at CNH for almost 20 years, explained the existing food service procedures. The kitchen is located below ground. He acknowledged that this layout was not uncommon when the facility was built, but the location is dark and damp according to current standards. The flooding about 6 years ago was like a nightmare. A large amount of food had to be discarded because of spoilage and the risk of contamination. An outside cleaning company had to be hired, and even then it required a lot of staff overtime to bring the kitchen into operation again. The residents were used to having home-cooked meals, and there was a lot of dissatisfaction with the food that was catered in. Mr. Washington fully supported the idea of moving the kitchen out of the basement, but he was not quite sure how the staffing for the four smaller kitchens would have to be planned. But, then, that was still a few years away! Ms. Morehouse stated that the main purpose of today’s meeting was to discuss the first phase of the project. This phase would be completed in two stages. In the first stage, the existing basement kitchen will be converted to a larger food storage and dishwashing area than what currently existed. A temporary kitchen would be built on the first floor. In the second stage, a household-style kitchen would be constructed by taking space from a portion of the current dining room on the first floor. She noted that during today’s meeting, the designers would begin discussion of their plans for this phase of the project. Mr. Hassan expressed some misgivings about this arrangement. He stated that he was not convinced that building a kitchen on every floor was the best use of financial and human resources. He noted that the first phase of the project alone would cost roughly $1,000,000. He also mentioned that other than the first floor, the other three floors simply did not have the space for a kitchen area. Mr. Washington responded that the current arrangement was outdated and that elimination of food carts would be a big plus for the facility. But he agreed that availability of space on the remaining three floors was a problem and he was not sure what would be the best solution. Ms. Laird stated that she was excited about the project. The aromas from meal preparation on the floors would create a homelike environment in the facility. Some of the residents could even help out and do minor chores in the kitchens if they so desired. Ms. Morehouse suggested that they discuss Mr. Hassan’s concerns at a later date since the board had already approved the construction budget for the first phase. She asked for an update from Mr. Morgan, Mr. Welbourne, and Ms. Reese. Mr. Welbourne informed the group that his team was ready to begin both the remodeling of the basement to create food storage and dishwashing areas. At the same time, construction of a temporary kitchen on the first floor would begin. He said that it would take about 5 months to complete this project. Once the basement and the temporary kitchen renovations were completed, a portion of the dining room would be blocked off to begin construction of the new household-style kitchen. He estimated that this stage would take an additional 3 months. Ms. Morehouse informed the group that therapy services would be moved and the temporary kitchen would be placed in that space. Ms. Laird questioned how noise, dust, security, and other potential disruptions would be handled during the construction. Mr. Welbourne said these considerations have been included in his plans, and he furnished some details. He requested that Ms. Laird should provide him with a list of any resident-related concerns and he would address those concerns before the next meeting. Ms. Smith said that she had become aware of some resident-related concerns. She stated that rehabilitation was using a large open area that has also been used as a multipurpose space for activities such as church services, meetings, games, parties, etc. She added that the activity director was upset that once the kitchen was moved to this location, the space would be too small to accommodate all of the residents. Mr. Welbourne suggested that perhaps activities could temporarily take place on the floors or in the residents’ rooms. Ms. Smith expressed concern that the residents may be isolated in their rooms. Ms. Morehouse stated that a solution to this would need to be explored. Ms. Reese and Mr. Morgan jointly presented the completed designs. Ms. Morehouse asked about the color scheme and overall kitchen aesthetics. Ms. Reese responded that her plan was to use colors consistent with the current facility color scheme given that the facility had been repainted less than a year ago. Ms. Morehouse said that the proposed color scheme would not be consistent with culture change. She offered to provide Ms. Reese with information on appropriate color schemes and other aesthetics consistent with culture change. Mr. Morgan explained that the kitchen would be equipped with commercial-style fixtures and appliances. He further stated that he was concerned that it sounded like the facility wanted something other than an institutional-type kitchen. Ms. Morehouse agreed that the kitchen fixtures and appliances needed to be chosen with the household model in mind. She asked if it would help if she provided him with some information detailing what type of fixtures and appliances would be appropriate for this style of kitchen. Mr. Morgan said he would welcome this information and attempt to make appropriate modifications with the understanding that all items must still meet NFPA and Life Safety Code® regulations. Ms. Morehouse asked whether there were any other concerns from anyone. Mr. Washington wanted to know whether the temporary kitchen on the first floor would be sufficient to prepare meals for 200 residents. Mr. Welbourne replied that the temporary kitchen was not meant for cooking that many meals. He said that the main use of the temporary kitchen would be for heating and serving meals, but it would not be equipped to prepare meals on a large scale. Mr. Washington stated that because the facility is required to provide hot meals, he would have to research other options. He further stated that because the kitchen staff would not be cooking meals during the building stage, each member of the kitchen staff would need new task assignments, because their essential jobs would change. The cooks, for example, would need new assignments because they would not be involved in meal preparation. Ms. Morehouse requested a report from him on the new task assignments. Ms. Smith stated that although she understood the reason the current therapy location was chosen for the temporary kitchen, her staff was not happy with the idea of moving. She further stated that the residents would need to be prepared for moving to a new location to receive therapy. Ms. Morehouse replied that she understood these challenges and would work with Ms. Smith to address staff and resident concerns. The meeting adjourned at 11:30 a.m. Following the meeting, Ms. Morehouse jotted down a list of things to do. As she pondered over it further, she was convinced that culture change was necessary, but wondered whether alternative plans should be explored.
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