b) Caitlyn has to determine how many of the 120 employees in her work place has comprehensive car insurance. She wants to obtain a sample of 40 employees. She selections employees from each department in proportion to the number of individuals the departments iv. Below are the number of individuals in each department Department Numbers Accounts 18 Marketing Sales Repairs 24 43 35 How many employees from the Marketing department should Caitlyn select to be part of the sample? Another employee suggested that Caitlyn should group employees by the type of car they own. State a reason why grouping the employees in this way will NOT be appropriate to select this sample using the sampling method in ii. V.
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- You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).Below is an excerpt from the article: Bennett, R. (2005). Factors associated with student plagiarism in a post-1992 university. Assessment & Evaluation in Higher Education, 30, 137-162.“There is a need for university staff to address forcefully the issue of academic integrity during introductory programs and to explain clearly and sympathetically the objective need for honesty in academic life” (p. 156).Which of the following examples correctly paraphrases the above passage without plagiarizing? Select one: a. During orientations, university staff should be very clear about the importance of academic integrity (Bennett, 2005). b. There is a need for colleges to forcefully address the issue of academic integrity during beginning programs and to explain clearly and sympathetically the objective need for integrity in college life (Bennett, 2005). c. There is a need for university staff to address forcefully the issue of academic integrity during introductory programs and to explain…A soup company wants to determine the optimal ingredients for its vegetable soup. The main ingredients are: Vegetables, Potatoes, Carrots, Onions, Meat, Water, Flavorings. The soup must meet the following specifications: A. No more than half of the soup can be vegetables B. The ratio of water to meat should be 8:1 C. The amount of meat should be between 5 & 6 percent of the soup D. The flavorings should weigh no more than ½ ounce The cost per ounce of the ingredients is $0.02 for the vegetables, $0.05 for the meat, $0.001 for water, and $0.05 for the flavorings. Formulate an LP model that will determine the optimal amounts of the various ingredients to achieve 15-ounce cans of soup at minimum cost
- Based on Carino and Lenoir (1988). BradyCorporation produces cabinets. Each week, Bradyrequires 90,000 cubic feet of processed lumber. Thecompany can obtain lumber in two ways. First, itcan purchase lumber from an outside supplier andthen dry it at the Brady kiln. Second, Brady canchop down trees on its land, cut them into lumber atits sawmill, and then dry the lumber at its kiln. Thecompany can purchase grade 1 or grade 2 lumber.Grade 1 lumber costs $3 per cubic foot and whendried yields 0.7 cubic foot of useful lumber. Grade 2lumber costs $7 per cubic foot and when dried yields0.9 cubic foot of useful lumber. It costs the company$3 to chop down a tree. After being cut and dried,a log yields 0.8 cubic feet of lumber. Brady incurscosts of $4 per cubic foot of lumber it dries. It costs$2.50 per cubic foot of logs sent through the sawmill.Each week, the sawmill can process up to 35,000cubic feet of lumber. Each week, up to 40,000 cubicfeet of grade 1 lumber and up to 60,000 cubic feetof…A large CPA firm currently has 100 junior staffmembers and 20 partners. In the long run—say,20 years from now—the firm would like to consistof 130 junior staff members and 20 partners. During a given year, 10% of all partners and 30% ofall junior staff members leave the firm. The firmcan control the number of hires each year and thefraction of junior employees who are promoted topartner each year. Can you develop a personnelstrategy that would meet the CPA firm’s goals?Problem 3: Let L(x, y) be the statement “x loves y”, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of the following statements.1. Everybody loves Jerry.2. Everybody loves somebody.3. There is somebody whom everybody loves.4. Nobody loves everybody.5. There is somebody whom Lydia does not love.6. There is somebody whom no one loves.7. There is exactly one person whom everybody loves.8. There are exactly two people whom Lynn loves.9. Everybody loves himself or herself.10. There is someone who loves no one besides himself or herself.
- Daniel Glaser, chairman of the College of San Antonio'sbusiness department, needs to assign professors to courses nextsemester. As a criterion for judging who should teach each course,Professor Glaser reviews the past 2 years' teaching evaluations(which were filled out by students). Since each of the four professorstaught each of the four courses at one time or another duringthe 2-year period, Glaser is able to record a course rating for eachinstructor. These ratings are shown in the following table.a) Find the assignment of professors to courses to maximize theoverall teaching rating.b) Assign the professors to the courses with the exception thatProfessor F isher cannot teach statistics.solve a and b The following table shows the rank attained by male and female officers in the NewYork City Police Department (NYPD).a) Do these data indicate that men and women are equitably represented at all levelsof the department? Test using a p-value approach. Male FemaleOfficer 21,900 4281Detective 4058 806Sergeant 3898 415Lieutenant 1333 89Captain 359 12Higher ranks 218 10 b) There are far more men than women in the police force in general. However, the NYCPolice Commission has set itself certain goals with respect to the positions of the femalesamong its ranks. Across the females they aim to target the same proportion by rank asthey do among the males. The target proportions by category are:(1) Officer – 70% (2) Detectives – 15% (3) Sargent – 10%(4) Lieutenant – 3% (5) Captain – 1% (6) Higher – 1%Conduct a test to determine whether the proportions,…Over a two-year period, the Topper Company sold the following numbers of lawnmowers:Month: 1 2 3 4 5 6 7 8 9 10 11 12Sales: 238 220 195 245 345 380 270 220 280 120 110 85Month: 13 14 15 16 17 18 19 20 21 22 23 24Sales: 135 145 185 219 240 420 520 410 380 320 290 240a. In column A input the numbers 1 to 24 representing the months and incolumn B the observed monthly sales. Compute the three-month moving-averageforecast and place this in the third column. Be sure to align your forecast with theperiod for which you are forecasting (the average of sales for months 1, 2, and 3should be placed in row 4; the average of sales for months 2, 3, and 4 in row 5; andso on.) In the fourth column, compute the forecast error for each month in whichyou have obtained a forecast.
- The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $1000 between newspaper advertising and radio advertising. Management decided that at least 25% of the budget must be spent on each type of media, and that the amount of money spent on local newspaper advertising must be at least twice the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from 0 to 100, with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is 50 and the value of the index for spot radio advertising is 80, how should the restaurant allocate its advertising budget in order to maximize the value of total audience exposure? a. Formulate a linear programming model that can be used to determine how the restaurant should allocate its advertising budget in order to maximize the value of total audience exposure. It's…1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars). (a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.(b) The quadratic function of best fit to these data isR(A) = - 7.76A2 + 411.88A + 942.72Use this function to determine the optimal level of advertising.(c) Use the function to predict the total revenue when the optimal level of advertising is spent.(d) Use a graphing utility to verify that the function given in part (b) is the quadratic function of best fit.(e) Use a graphing utility to draw a scatter diagram of the data and then graph the quadratic function of best fit on the scatter diagram.