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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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- Show detailed calculation Capacity ManagementTo minimise the labour cost of every customer service centre throughout the country, LG ElectronicsVietnam runs a single-server system. A single-server queue has random arrivals at a rate of 30 an hourand random service times at a rate of 40 an hour. If it costs £20 for each hour a customer spends in thesystem and £40 for each hour of service time, how much does the queue cost?The production planning period for flat-screen moni-tors at Louisiana’s Roa Electronics, Inc., is 4 months. Cost data are as follows:Regular-time cost per monitor $ 70Overtime cost per monitor $110Subcontract cost per monitor $120Carrying cost per monitor per month $ 4 For each of the next 4 months, capacity and demand for flat-screen monitors are as follows: PERIOD MONTH 1 MONTH 2 MONTH 3 a MONTH 4Demand 2,000 2,500 1,500 2,100CapacityRegular time 1,500 1,600 750 1,600Overtime 400 400 200 400Subcontract 600 600 600 600aFactory closes for 2 weeks of vacation.CEO Mohan Roa expects to enter the planning period with 500monitors in stock. Back ordering is not permitted (meaning, forexample, that monitors produced in the second month cannot beused to cover first month’s demand). Develop a production planthat minimizes costs using the transportation method.A Manufacturing Corp. with three-station work cell has the process displayed below. Each workstation has only one worker to the assigned activity. Single order arrives every 7.5 hours. c) What is the cycle time corresponding to maximum throughput and actual throughput?d) Suppose that a second parallel machine is added at station 2. What is the new bottleneck timeand new throughput time of the system? How did the addition of the second machine at workstation 2 affect the performance of the work cell? IN Station 1 OUTTask Time: 3 hrs.Station 2Task Time: 5 hrs.Station 3Task Time: 2 hrs.
- A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapse from when the customer enters the queue until he/she reaches the teller’s window. In addition, suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 pm lunch period and data were collected at random at these branches and recorded below; No of Customers Commercial dist branch (time) Residential area branch (time) 1 – 5 3 3 6 - 10 5 6 11 - 15 8 5 16 – 20 8 3 21 - 25 4 2 Required Which of the branches has a relatively better mean waiting time? Which shop can be surer of meeting the mean waiting time at the two branches? Assuming…A municipal solid-waste site for a city must be located at Site A or Site B. After sorting, some of the solid refuse will be transported to an electric powerplant where it will be used as fuel. Data for the hauling of refuse from each site to the power plant are shown in Table P2-4. If the power plant will pay $8.00 per cubic yard of sorted solid waste delivered to the plant, where should the solid-waste site be located? Use the city’s viewpoint and assume that 200,000 cubic yards of refuse will be hauled to the plant for one year only. One site must be selected.The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 750 homeless patients and no more than 900 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,500 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients: homeless: profit:
- A service has five tasks, performed in sequence. In the instance when there is more than one worker assigned to a task, each worker performs the entire task and they both can be working on different “items” at the same time. Task Task time per worker Number of workers 1 2 minutes 1 2 6 minutes 1 3 14 minutes 2 4 4 minutes 1 5 15 minutes 3 What is the capacity (hourly) of the process as a whole? What is the bottleneck of the process? What is the throughput time (assuming no wait time)? Where would you expect customers to wait?The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit? Group of answer choices A)700 homeless patients and 1,100 high-income patients B)1,200 homeless patients and 600 high-income patientsC)700 homeless patients…The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit?