GLS UNIVERSITY S FACULTY OF COMMERCE B. COM. SECOND YEAR SEMESTER IV STATISTICS FOR BUSINESS AND MANAGEMENT OBJECTIVE QUESTIONS

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1 Q.1 Choose the correct options: GLS UNIVERSITY S FACULTY OF COMMERCE B. COM. SECOND YEAR SEMESTER IV STATISTICS FOR BUSINESS AND MANAGEMENT OBJECTIVE QUESTIONS Unit: 1 Differentiation and Applications of Differentiation 1. The derivative of x 2 w.r.t. x is. A. x B. 2x C. x-1 D. x+1 2. The derivative of 100 w.r.t. x is. A. Zero B. 100 C D. C 3. The derivative of log x w.r.t. x is. A. 1 1 B. C. 2 x x 2 x D. 2x 4. State the derivative of 7x w.r.t. x A. 7x B. 14x C. 14x+13 D. None of these 5. If f(x)=9x 3 +3 x 2-2 x -13, find f (0). A. (-26) B. 26x C. (-13) D For what value of x, the derivative of f(x)=2x 2-8x+17 will be zero? A. 4 B. 16 C. 16x D For what value of x, the derivative of f(x)=4x 2-32x-100 will be zero? A. 8x B. 8 C. 32x D What is the value of log e e? A. 1 B. 0 C. e D. log e 9. What is the derivative of e 2x? A. e 2x B. 2 e 2x C. e x D. None of these 10. Give the derivative of 7 x w.r.t. x. A. 7 x log 7 B. 7 x C. log 7 D. 7 log 7 Q.2 Do as directed: 1. If f(x)=x 2 +5, then f (1) = 2.

2 dy 2. If y = x 3 x 2-3 x + 8 and = ( 6), then x = 1. dx 3. The derivative of log e e w.r.t. x is Zero. 4. If f(x) = 9x -36 and f(x) = f (x) then x = The derivative of e e w.r.t. x is Zero. 6. The derivative of x e w.r.t. x is ex e The derivative of x a + a x + a a w.r.t. x is ax a-1 + a x log a. 8. The ratio of percentage change in supply to percentage change in the price of a commodity is called as Elasticity of Supply. 9. If elasticity of demand e > 1, then demand is said to be relatively elastic. 10. If elasticity of demand e = 1, then demand is said to be unitary elastic. Q.3 Answer the following: 1. Give the relationship between Marginal Revenue, Average Revenue and Elasticity of Demand. Ans: η = AR AR MR 2. Find elasticity of supply at p=2 if the supply function is x = 5 + 2p 2. Ans: Elasticity of supply 1.23 =. 3. For what value of x, f (x) = f (x) for the function f(x)= x 3-24x Ans: x= (-2) or x=4 4. Interprete elasticity of demand = 0.8 Ans: Since 0.8 < 1, the demand is relatively inelastic Is the function p = 13 a supply function? x Ans: No, since in the above function price p and demand x are inversely proportional to each other.

3 Q.1 Choose the correct options: Unit: 2 Process Control Techniques Statistical Quality Control 1. developed the technique of quality control to know whether the products are of standard quality or not. A. Shewhart B. Pearson C. Fisher D. Spearman 2. In India, the use of statistical quality control was introduced by. A. Mahalanobis B. Laplace C. Paasche D. Bowley 3. The charts based on quality characteristics are called as charts. A. Variable B. Attribute C. Quality D. Acceptance 4. p chart is a chart of. A. Fraction Defective B. Number of defectives C. Defects D. None of these 5. The quality of the samples of low spots are considered to be. A. Inferior B. Superior C. Moderate D. None of these 6. In X chart, if any of the sample points go beyond U.C.L. and L.C.L. then the process is said to be out of control w.r.t.. A. Variable B. Range C. Average D. None of these 7. In X chart, if UCL = 30 and = 20 X LCL then central line =. A. 50 B. 27 C. 25 D In R chart, if R =10, D 3 =0, D 4 =2.11 then LCL=. A. 0 B C. 10 D. 20 X 9. The points falling outside control limits show presence of causes of variation. A. Chance B. Random C. Assignable D. None of these 10. distribution is used in the construction of np chart. A. Poisson B. Binomial C. Normal D. Geometric Q.2 Do as directed: 1. Attribute charts are less sensitive as compared to the variable charts. 2. Variable charts can be used when the quality characteristics are measurable. 3. The theory of Normal distribution is used in X and R charts.

4 4. p, np and C are the charts for attributes. 5. C chart can be used to control the production process for the number of defects in television sets. 6. More time and money are required in variable charts as compared to attribute charts. 7. The theory of Poisson distribution is used in C chart. 8. If C =36, then the lower control limit of C chart will be From a production process 10 samples each of size 100 are taken and the average fraction defective is found to be Then the central line of np chart will be In R chart, if some of the sample points fall outside the control limits then it can be concluded that there is significant variations within the samples. Q.3 Answer the following: 1. In X chart if UCL = 80 and LCL =72 then find the value of central line. Ans: State the upper control limit of p chart. Ans: UCL = p + 3 p(1 p) n 3. State any two reasons for assignable causes of variations. Ans: Difference in quality of raw materials and Difference in machines 4. Expalin Theory of Run. Ans: The falling of consecutive points on the same side of the central line is said to be a run. If they fall on the upper side of the central line it is said to be a Run Above and if they fall on the lower side of the central line it is said to be Run Below. 5. Sate the upper and lower control limit of np chart. Ans: UCL = n p + 3 n p(1 p ) LCL = n p 3 n p(1 p )

5 Q.1 Choose the correct options: Unit: 3 Product Control Techniques Acceptance Sampling 1. The process of deciding about the acceptance or rejection of the lot on the basis of sample inspection is known as. A. Decision Sampling B. Acceptance Sampling C. Quality Control D. None of these 2. In a single sampling plan (2000, 150, 4), what is the size of the lot? A. 150 B C. 4 D For a single sampling plan (1000, 20, 4), what will be the value of ASN? A B. 4 C. 20 D Under a given sampling plan, the maximum value of is called as Average Outgoing Quality Level. A. AOQ B. ASN C. LTPD D. ATI 5. For a single sampling plan (150,20,3), what is the value of acceptance number? A. 150 B. 3 C. 60 D If the probability of acceptance is 0.85 and the proportion defective is 5%, then find the value of AOQ. A B C D For a single sampling plan (150, 20, 3) the probability of acceptance is 0.95, calculate ATI. A B. 30 C D If ASN of a single sampling plan is 20, find the sample size. A. 25 B. 60 C. 20 D If the maximum value of an AOQ curve is 0.75, then find the value of AOQL. A B C D State the formula of ATI. A. n + (N n)(1 P a ) B. (N n)(1 P a ) C. n - (N n)(1 P a ) D. n - (N + n)(1 P a ) Q.2 Do as directed: 1. The probability of rejecting a good lot is known as Producer s Risk. 2. The performance of any plan can be judged by its Operating Characteristic Curve. 3. The level denoting good quality is known as Acceptance Quality Level(AQL).

6 4. The full form of LTPD is Lot Tolerance Proportion Defective. 5. In any sampling plan the average number of units inspected is called as Average Sample Number. 6. The full form of AOQ is Average Outgoing Quality. 7. The probability of accepting a lot of bad quality is known as Consumer s risk. 8. An acceptance sampling is an understanding between a producer and a consumer about the acceptance or rejection of the lot. 9. When the proportion defective is 0, the value of P a will be For a given lot and for a fixed value of n as the value of acceptance number c decreases the size of the curve decreases. Q.3 Answer the following: 1. If the proportion defective is 2% and probability of accepting the lot is 0.8 then calculate the value of AOQ. Ans: AOQ = p P a = 0.02*0.8 = For a single sampling plan (100,25,4), if the probability of accepting the lot is 0.31 then calculate the value of ATI. Ans: ATI = n + (N n)(1 P a ) = 25 + (100-25)(1-0.31) = If probability of accepting the lot is 0.81, calculate Producer s risk. Ans: Producer s Risk α = = The ATI s of three different plans A, B and C are 454, 343 and 331 respectively. Which plan should be suggested to a producer? Ans: As ATI for plan C is minimum, so it should be suggested to the producer. 5. Define double sampling plan. Ans: The process of taking decision for accepting or rejecting the lot based on two samples is known as double sampling plan.

7 Unit: 4 Decision Theory Q.1 Choose the correct options: 1. In principle, α is called as the Coefficient of Optimism. A. Maxi-min B. Maxi-max C. Laplace D. Hurwitz 2. If the minimum pay-offs of five different acts P, Q, R, S and T are 15, 12, 9, 11 and 10 respectively. Then which act should be selected according to Maxi-min principle? A. P B. Q C. R D. S 3. If the probabilities for two states of nature are 0.55 and If the payoffs for an act are 95 and 107, then find EMV. A. 90 B C D In which principle of decision making coefficient of optimism is selected? A. Laplace B. Hurwitz C. Maxi-min D. Maxi-max 5. If the future demands are not known with certainty one would select the lot with maximum. A. EVPI B. EPPI C. EMV D. None of these 6. If the maximum payoffs of different acts E, F, G, H and I are 13, 17, 11, 19 and 20 respectively. Then according to Maxi-max principle which act should be selected? A. F B. G C. H D. I 7. If EMV for 4 different acts are 35, 40, 55 and 70 and EVPI = 15, find Expected Profit for Perfect Information. A. 80 B. 85 C. 75 D The arrangement of different payoffs from different states of nature and acts is known as a matrix. A. Pay-off B. Interest C. Dividend D. Percentage 9. EPPI Max EMV =. A. EVPI B. MEMV C. EMVI D. None of these 10. The selection of any act depends upon the states of nature which are not in the control of the. A. Decision Maker B. Administrator C. Employee D. Accountant

8 Q.2 Do as directed: 1. The monetary gain or loss from the combination of state of nature and act is known as its Pay off. 2. The probability of different states of nature are only the estimates. 3. The situation in which the decision maker cannot access the probabilities of the various states of nature are called as decisions under uncertainty. 4. In decion theory the acts are also termed as strategies. 5. Maxi-min principle is the pessimistic approach towards the selection of the act. 6. Hurwitz s principle is a compromise between optimistic approach of maxi-max principle and pessimistic approach of maxi-min principle. 7. In Laplace principle equal probabilities are assigned to different states of nature. 8. Expected monetary value is calculated for the decision under risk. 9. A decision tree has three main elements namely acts, events and outcomes. 10. Decision tree draws immediate attention to the decision to be made and thus it helps management to avoid wasting of time. Q.3 Answer the following: 1. The maximum and minimum pay-offs of 5 different acts are given in the following table. If the coefficient of optimism α=0.3, which act should be selected according to Hurwitz s Principle? Ans: P Q R S T Maximum Payoff Minimum Payoff P Q R S T Maximum Payoff Minimum Payoff According to Hurwitz s principle act R should be selected.

9 2. For the following pay off for an act EMV is 500. Find x. States of nature A B C Probabilities Pay-off x Ans: 0.3x + (0.2*325) + (0.5*520) = 500 Hence, x= If EMV for the acts are 100, 150, 160, 90 and 140 and EPPI = 180. Find the value of EVPI. Ans: EVPI = EPPI Max EMV = = Write any two advantages of decision tree. Ans: 1. Decision tree is an useful management tool. 2. Decision tree is useful where a problem has its solution in recurring type of decisions. 5. Write the full forms of EVPI and EMV. Ans: EVPI = Expected Value of Perfect Information EMV=Expected Monetary Value *******