THE UNIVERSITY OF THE WEST INDIES (DEPARTMENT OF MANAGEMENT STUDIES)

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1 THE UNIVERSITY OF THE WEST INDIES (DEPARTMENT OF MANAGEMENT STUDIES) Mid-Semester Exam: Summer2005 June 20:2005; 7:00 9:00 pm MS 23C: Introduction to Quantitative Methods Instructions 1. This exam has XXX pages and 30 questions. 2. This accounts for XXX% of your final grade. 3. You have two hours to complete this exam. 4. Write and SHADE in your ID number on the answer sheet (in the spaces provided). 5. Shade in your response to each of the questions on the answer sheet provided. 6. No point will be deducted for an incorrect response. 7. Scientific Calculators are allowed. 8. A formula sheet is attached at the back 9. Standard Normal (Z) tables are at the back 1

2 Q1. A teacher has a number of students scores to which she wants to assign a grade. Her grading scheme is like this: If the student scores between 90 and 100, both inclusive, the student gets an A; between 80 and 89, both inclusive, B+; between 70 and 79, both inclusive, B; between 60 and 69, both inclusive, B ; between 50 and 59, both inclusive, C+; between 40 and 49, both inclusive, C and under 40, F. Which of the following would give the correct table if she wanted to use VLookup to assign grades? 1) A 2) B 3) C 4) D A B C D Range Grade Range Grade Range Grade Range Grade 100 A 0 F 40 F 0 F 90 B+ 39 C 50 C 40 C 80 B 49 C+ 60 C+ 50 C+ 70 B- 59 B- 70 B- 60 B- 60 C+ 69 B 80 B 70 B 50 C 79 B+ 90 B+ 80 B+ 40 F 89 A 100 A 90 A Copycat Retailing is trying to manage its inventory by implementing a (Q, R) policy, where Q = the amount to order each time an order is placed and R = the Reorder Point the level to which the inventory falls before it triggers an order. Copycat monitors its costs [Stockout ($40): when available inventory cannot meet demand; Order ($100): the cost incurred whenever an order is placed and Inventory ($15): calculated on ending inventory]. It is hoped that the total costs can be minimised by the appropriate choice of Q and R, which are initially set at 70 and 50, respectively. Assume that all orders placed are received first thing the next week, in the ten week analysis shown below. Demand was forecasted as shown. Opening Stock is 80 units, and the exhibit below shows the details of the case. Sales are made based on available inventory and demand. Order? 1 = Yes; 0 = No. Answer the following questions: Q2. What formula goes in F9? Select the best possible answer. A. =D9 B. =IF (D9 E9, D9, E9) C. =MIN (D9, E9) D. =IF (D9 B9+C9, D9, B9+C9) 1) C only 2) Either B or C 3) Either B or C or D 4) B only 2

3 Q3. What formula goes in H9? Select the best possible answer. A. =E9 F9 B. =MAX (E9 F9, E9 D9) C. =MAX (E9 F9, 0) D. =IF (E9 D9, E9 D9, 0) 1) Either C or D only 2) B only 3) D only 4) None of the above Q4. What formula goes in I9? Select the best possible answer based on good spreadsheet principles. 1) =IF (H9 70, 1, 0) 2) =IF (H9 B4, 1, 0) 3) =IF (H9 < 50, 1, 0) 4) =IF (H9 = B4, 1, 0) 3

4 Q5. Using the same case, Copycat wants to evaluate different order quantities to see the effect on average closing inventory and will do so in cells A23:B29, what Function & formula will be tried? 1) Data Table, Set Cell = H19, Changing cell = B4 2) Data Table, B23 = B4, Row input = H19 3) Data Table, B23 = H19, Column input = B4 4) Data Table, B23 = M19, Column input = H19 The above spreadsheet has a list of cars (Make, Model, Date, Quantity, and Value). The database goes from A1:E40 with row one (1) having the headings. The makes are Toyota, China Town, BMW, Nissan, Honda and Suzuki. The China Town model is a clone sold in Asia and parts of the Caribbean. They copy the brand name cars and sell them profitably, without having invested in research and development. Some of their models are Camry, Prado, Cefiro and X-Trail. Answer questions 6 and 7 all based on SUMPRODUCT 4

5 Q6. In trying to determine the TOTAL value of all Toyota Prados sold, which function is correct? Total Value is quantity * value 1) = SUMPRODUCT (($A$2:$A$40= Toyota )*($B$2:$B$40= Prado )*($D$2:$D$40)* ($E$2:$E$40)) 2) = SUMPRODUCT (($B$2:$B$40= Prado ) *($D$2:$D$40)*($E$2:$E$40)) 3) = SUMPRODUCT ($A$2:$A$40= Toyota )+ SUMPRODUCT (($B$2:$B$40= Prado )*($E$2:$E$40)) 4) = SUMPRODUCT (($A$2:$A$40= Toyota )*($B$2:$B$40= Prado )*($E$2:$E$40= Value ) *($D$2:$D$40)) Q7. In trying to determine the total value of all vehicles sold, which function is correct? 1) = SUMPRODUCT (($A$2:$A$40="Nissan")*($B$2:$B$40="X-Trail")*($E$2:$E$40)) + SUMPRODUCT (($A$2:$A$40="Toyota")*($B$2:$B$40="Prado")*($E$2:$E$40)) etcetera. That is, do so for each make and model 2) = SUMPRODUCT (D2:D40,E2:E40) 3) All of the above 4) None of the above Q8. Which of the following statements is/are true about Goal Seek? A) Goal Seek is used to determine a single output from several inputs B) The Set Cell must be a cell that contains a formula, function or cell reference. C) The By Changing Cell must be a number or a blank cell. It cannot contain a formula, function or cell reference D) The set cell must be referenced by formula to the By Changing Cell 1) All of the above 2) B, C and D only 3) B only 4) A, C and D only Q9. Which of the following statements is/are true about Data Tables? A) Two way data tables have two outputs and one input B) They do what-if analyses. C) One way data tables have many outputs but one input D) Two way data tables have two inputs and one output. 1) B and D only 2) All of the above 3) B, C, and D only 4) A, B and D only 5

6 Q10. It has been determined that there is a 65% chance an investor will place her money with JMMB if economic conditions remain the same; a 25% chance of placing her money with JMMB if economic conditions decline and a 50% chance of placing her money with JMMB if economic conditions improve. Analysis has placed the probability of economic conditions remaining the same at 50%; of declining at 20% and of improving at 30%. What is the probability the investor will place her money with JMMB? [One point given to everyone] 1) ) ) ) Q11. If two events are mutually exclusive, then 1) Their probabilities can be added 2) Their events are dependent 3) They cannot have a joint probability 4) All of the above Q12. The probability of Gunman X being caught by Kingfish is 0.4; the probability of Gunman Y being caught by Kingfish is 0.5; the probability of both being caught by Kingfish is 0.2 A) These events are independent B) These events are dependent C) The probability that X will be caught given that Y is already caught can be determined D) The probability of at least one being caught is 0.7 1) A, C and D only 2) B and D only 3) A and D only 4) B and D only Q13. A production process produces items such that 10% are always defective. If two items are randomly selected off the production line, what is the probability that exactly one of these is defective, (either the first is defective and the second is not, or the second is defective, and the first is not, but not both) assuming independence 1) ) ) )

7 Q14. A company is considering some new products which have a 60% chance of being successful in the market and a 40% chance of failure. Market research may be conducted and history shows that the probability is 90% the market research will say good given that the product was successful and probability is 20% the market research will say good given that the product was a failure. Suppose the market research was done and it said good, what is the probability the product was a success? 1) ) ) ) 0.87 Q15. What value must p take to make P(x) a probability distribution? 1) ) ) ) 0.08 x P(x) p 0.23 Q16. Refer to the question above, what is the Expected Value of the random variable X? 1) ) ) ) 4.56 Q17. Refer to the question above, what is the variance? 1) ) ) ) Q18. Refer to the question above, what is the coefficient of variation? 1) ) ) )

8 Q19. A continuous random variable is one that 1) Can assume only a finite set of values 2) Has an infinite set of values 3) Can be described by a probability distribution 4) May be a multinomial random variable Q20. The following is NOT true about continuous random variables 1) The area under each of the curve represent probabilities 2) Some may be described by uniform and exponential distributions 3) The entire area under each curve equals one 4) They are useful to describe a discrete probability distribution Q21. The time taken to complete a project is described by a normal distribution with mean of 80 weeks and a standard deviation of 10 weeks. What is the probability the project is finished in 70 weeks or less? 1) ) ) ) Q22. The time taken to complete a project is described by a normal distribution with mean of 80 weeks and a standard deviation of 10 weeks. The company will pay a penalty if the project is not finished by the due date in the contract. They want to be 90% sure of finishing by the due date. What due date should be negotiated? 1) ) ) ) Q23. The time taken to complete a project is described by a normal distribution with mean of 80 weeks and a standard deviation of 10 weeks. What is the probability the project takes between 81 and 92 weeks to be completed? 1) ) ) ) Q24. Arrivals by students at DOMS front desk for advice in registration week are known to average 4 persons per 10 minutes. What is the probability that in a registration week, 9 students arrive to ask for advice in 30 minutes? 8

9 1) ) ) ) cannot be determined Q25. A construction company has recently built a hotel. The probability that the new hotel will get an award for its design is 0.28, and the probability that it will get an award for the efficient use of materials is If the probability that it will get at least one award is 0.36, what is the probability that it will get both awards? 1) ) ) ) 0.49 Q26. Which of the following is not a true probability distribution? 1) A, B, C, D 2) B and D 3) B, C and D 4) B only a P(a) b P(b)) c P(c) d P(d) Q27. It is known that 5% of all watches produced by a certain company are defective. What is the probability that in the quality control programme, 4 watches are inspected before the first defective one is found? 1) ) ) ) Q28. It is known that 15% of all watches produced by a certain company are defective. What is the probability that in the quality control programme, in a random sample of 12 watches, 4 are found to be defective? 1) ) ) ) None of the above 9

10 Q29. A company is considering producing some new products. Based on past records, management believes that there is a 60 percent chance that the first product will be successful, and a 40 percent chance that the second product will be successful. It is also known that the probability that both are successful is Suppose the second product was found to be successful, what is the probability the first will be successful? 1) ) ) ) 0.75 Q30. It is known that 40% of all new companies fail after startup within one month. In a random sample of size 50 of startups made less than a month, what is the probability that the researchers will find that 15 companies failed? Which distribution can be used to answer this question? A) Geometric B) Poisson C) Binomial D) Multinomial 1) C only 2) B and C only 3) B, C and D only 4) A, B and C only END OF EXAM! 10

11 Some Probability Formulae...(1)...(2)...(3)...(4)...(5)...(6)...(7)...(8)...(9)...(10)...(11)...(12) ;...(13)...(14)...(15) ; 11