Concept explainers
In this chapter, we noted the importance of defining and analyzing a problem prior to attempting to find a solution. Consider this example: One of the earliest operations research groups during World War II was conducting a study on the optimum utilization of Spitfire and Hurricane aircraft during the Battle of Britain. Whenever one of these planes returned from battle, the locations of the bullet holes on it were carefully plotted. By repeatedly recording these data over time, and studying the clusters of data, the group was able to estimate the regions of the aircraft most likely to be hit by enemy gunfire, with the objective of reinforcing these regions with special armor. What difficulties do you see here?
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Business Analytics, Loose-leaf Edition (3rd Edition)
- A manufacturing company is analyzing its accident record. The accidents fall into two categories: Minor—dealt with by first aider: Average cost k50 Major—hospital required. Average cost k1,000The company has 1,000 employees, of which 180 are office staff and the rest work in the factory.The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year.(i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii)Show that the probability that a given a member of office staff has an accident in a year is 0.0549.(iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.arrow_forwardQuestion 1 Stopping Distances In a study on speed control, it was found that the main reasons for regulations were to make traffic flow more efficient and to minimize the risk of danger. An area that was focused on in the study was the distance required to completely stop a vehicle at various speeds. Use the following tables to answer the questions. MPH BRAKING DISTANCES (FEET) 20 20 30 45 40 81 50 133 60 205 80 411 Assume MPH is going to be used to predict stopping distance. Calculate the correlation coefficient ‘r’ for these values. What does a correlation coefficient tell about the relationship between two variables? Within what range can a correlation coefficient assume a value. Will you expect a positive, negative or zero correlation between the two variables for each of the following examples Variables Type of Correlation Grade of a student and hours spent studying Incomes and entertainment expenditures of…arrow_forwardA company that operated 10 hours a day manufactures two products on three sequential processes. The following table summarizes the data for the problem: Please answer the two questionsarrow_forward
- Question 6 In an effort to reduce the number of hospital-acquired conditions (such as infection resulting from the hospital stay), Medicare officials score hospitals on a 10-point scale with a lower score representing a better patient track record. The federal government reduces Medicare payments to those hospitals with the worst scores. The following data represent the scores received by Illinois hospitals. Score 1-1.9 2-2.9 3-3.9 4-4.9 5-5.9 6-6.9 7-7.9 8-8.9 9-10 Total Frequency 3 12 16 23 23 21 17 5 5 125 a) Determine the probability that a randomly selected hospital in Illinois has a score between 7 and 7.9. b) Determine the probability that a randomly selected hospital in Illinois has a score that is not between 7 and 7.9. c) Determine the probability that a randomly selected hospital in Illinois has a score less than 5.arrow_forwardChapter 14 #1 Problem 11 [page 620] To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models. Brand & Model Price ($)Overall Score Samsung Ultrabook NP900X3C-A01US Apple MacBook Air MC965LL/A Apple MacBook Air MD231LL/A HP ENVY 13-2050nr Spectre XT Sony VAIO SVS13112FXB Acer Aspire S5-391-9880 Ultrabook Apple MacBook Pro MD101LL/A Apple MacBook Pro MD313LL/A 1250 83 1300 83 1200 82 950 79 800 77 1200 74 1200 74 1000 73 Dell Inspiron I13Z-6591SLV Samsung NP535U3C-A01US 700 67 600 63 Use the least squares method to develop the estimated regression equation (by Hand calculations). a. b. Another laptop that Consumer Reports tested is the Acer Aspire S3-951-6646 Ultrabook; the price…arrow_forwardQuestion 2. An engineer wants to determine how the weight of a car affects gas mileage. The following data represent the weights of various domestic cars and their gas mileages in the city for the 2015 model year. (Using Excel) Car Buick Lacrosse Cadillac XTS Chevrolet Cruze Chevrolet Impala Chrysler 300 Dodge Charger Dodge Dart Ford Focus Ford Mustang Lincoln MKZ Weight(lb) 4724 4006 3097 3555 4029 3934 3242 2960 3530 3823 Miles per Gallon 17 18 22 19 19 19 24 26 19 18 a) Determine which variable is the likely explanatory variable and which is the likely response variable. b) Draw a scatter diagram of the data. (Add the axis title) c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon in the city. (4 decimal) d) Does a linear relation exist between the weight of a car and its miles per gallon in the city? Why? e) Suppose that we add the Ford Fusion Hybrid to the data. A Fusion Hybrid weight 3639 pounds and gets 44 miles per gallon. Redraw…arrow_forward
- A quality control engineer studied the relationship between years of experience as a system control engineer and the capacity of the engineer to complete within a given time a complex control design including the debugging of all computer programs and control devices. A group of 25 engineers having widely differing amounts of experience (measured in months of experience) was given the same control design project. The results of the study are given in the following table with y 5 1 if the project was successfully completed in the allocated time and y 5 0 if the project was not successfully completed. a. Determine whether experience is associated with the probability of completing the task. b. Compute the probability of successfully completing the task for an engineer havingarrow_forwardA manufacturing company is analyzing its accident record. The accidents fall into two categories: Minor—dealt with by first aider: Average cost k50 Major—hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. [] On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.arrow_forwardThe attached file contains hypothetical data for working this problem. Goodman Corporation’s and Landry Incorporated’s stock prices and dividends, along with the Market Index, are shown in the file. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends. Construct a scatter diagram graph that shows Goodman’s and Landry’ returns on the vertical axis and the Market Index’s returns on the horizontal axis.arrow_forward
- THE FOLLOWING FIGURE IS USED TO ANSWER THE FOLLOWING QUESTION. The percentage of deaths due to pneumonia, Influenza, and COVID-19: Figure 1 NCHS Mortality Reporting System: Pneumonia, Influenza, and COVID-19 Mortality of Deaths Due to Poeumonia, influents, and COVID-19 * * 12 30 40 NCHS Mortality Reporting System: Pneumonia, Influenza, and COVID-19 Mortality Data through the week ending April 11, 2020, as of April 16, 2020 50 Tidenk Threshold Seasonal Baseline 2018 10 20 50 -% of Deaths due to Pneumoni, Influenx or COVID-19 30 MMWK Week was higher than expected for the majority of 2018 and 2019. W in week 10 of 2020 was roughly 3X greater than expected. O on average met the level of epidemic in week 20 of 2019 O is highest mid-year and lowest at the end of each year.arrow_forwardDrop-off points (points de collecte in French), where residents can dispose of their organic waste for composting, were established in each of the five targeted neighborhoods of PROBLEM 1. Camille wants to see whether or not there exists a relationship between the average weekly amount of non-disposed food waste per household and the availability of drop-off points in the neighborhood, expressed as the number of households per drop-off point (considered fixed). Her data and some of her preliminary calculations are presented below: Number of Amount of non- (x, – x)* (Y, -Y) (x; - x)(Y, – Y) households per drop-off point disposed food waste per household (kg/week) Yi Xi 387.5 4.0 7656.25 0.25 43.75 337.5 3.2 1406.25 0.09 -11.25 187.5 2.5 12656.25 1.00 112.50 412.5 5.0 12656.25 2.25 168.75 175.0 2.8 15625 0.49 87.50 E; = 1500 Σ 17.5 E; = 50000 Σ -4.08 Ej = 401.25 2) Camille also calculated the slope of the fitted regression line: estimated slope = 0.008. Test whether or not the…arrow_forwardResearchers were interested in better understanding how autistic children see and understand the world. Participants included children diagnosed with autism and typically- developing children, who were all approximately the same age. All children were presented with several different stimuli on a large computer screen for up to one minute. The stimuli were both social (i.e., people’s faces) and nonsocial (inanimate objects). The percentage of time children spent looking at the two types of stimuli was recorded (ranging from 0 to 100). Consider the graphs shown for a study about blaming the victim. a. What is proper statistical the notation of the design? Use the “__ × __” format. b. Interpret the graphs for the blaming the victim study. For each graph, what are the significant main effects? Is there an interaction? Interpret the main effects and interactions that are present.arrow_forward
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