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    Previous solved paper,quantitative methods i sem,  exam jan 2011 mba , mdu rohtak , dde Previous solved paper,quantitative methods i sem, exam jan 2011 mba , mdu rohtak , dde Document Transcript

    • Shakehand with LifeQuantitative Methods/TechniquesComplete Solved Question PapersM.B.A 2yrs (1st Semester) (DE)Maharishi Dayanand University, Rohtak JANUARY 2011 Year 2011 Solved by Narender SharmaQuality Professional in a leading Container Glass Manufacturing Organization HNG Industries Ltd , Bahadurgarh www.shakehandwithlife.blogspot.com
    • Few wordsTo All Management and Engineering Professionals………………All of you have studied about the Software and Hardware as these understand as a heavy source of earningbut I believe in Humanware and in my view “Nothing costly than a human mind as it has unlimitedcapabilities.” so my Mission statement is “Shakehand with Life”All Calculations and graphs in these papers have made with the help of MS – Excel and Advanced StatisticalSoftware Minitab and every precaution has been taken while solving the questions. I assure you that you willscore maximum marks in your Q.T. examination very easily through these papersAs a quality professional It is my effort to induce the statistical temperament in the minds of all managementand engineering professionals who are coming in management programme from different corporate areas.Statistic is the basic tool to reach on a precise and specific decision, as decision making is the key responsibilityin the management. If you are not aware about the role of Statistic in the management then definitelysomewhere you will lag behind in your area.I always seeking the feedback from your side so that, I can continuously make improvement in my work.With RegardsNarender Sharma Working As A Quality Professional In A Leading Container Glass Manufacturing Organization Since July 2001 To Till Date. Visiting Faculty in Leading Management Institutes in Delhi. Six –Sigma Green Belt. Group Member “Benchmark Six Sigma” , “Leaders Think Tank” on Linkedin. M.B.A. (Production And Operation Management). B.Sc. (Electronics, Physics, Mathematics). B.Ed. ( Teaching of Mathematics, Teaching of Science)Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 1www.shakehandwithlife.blogspot.com
    • Few Motivational words “ I know you are going to make it ……….. It may take time and hard work You may become frustrated and at times you will feel like giving up Sometimes you may even wonder if it’s really worth it But I have confidence in you and I know you’ll make it, If you try.” ……………..Ananda Pierce Train-ed To be a LeaderPeople are often like a Train, Some are like its EngineLeading the train forward,Some are like bogies chugging along, following the leaderWhile few others are likes the brakes, putting a stop to its motionTherefore the leader is like the Engine of this trainA man who will lead with trust and honesty,with speed and also ensure that there are no accidents. Narender Sharma Lead India MAILBOX, My Times, My Voice Times of India, New Delhi, Aug24, 2007, p. 2“You see things ; and you say, ‘why?’ But I dreams things that never were; and I say, “why not?”Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 2www.shakehandwithlife.blogspot.com
    • Unit I Functions –meaning, types, and their business applications Arithmetic progression, Geometric progression , and their business application Matrices and their business applicationUnit II Construction of frequency distribution and their analysis in form of measures of central tendency and variations Types of measures , their relative merits, limitations and characteristics Skewness , meaning and coefficients of skewness.Unit III Correlation analysis-meaning and types of correlation Karl Pearson’s co-efficient of correlation and Spearman’s rank correlation Regression Analysis-meaning and two lines of regression Relationship between correlation and regression co-efficients. Time series analysis-measurement of trend and seasonal variations, time series and forecasting.Unit IV Probability-Basic concepts and approaches, addition , multiplication. Bayes’ theorem. Probability Distribution-Meaning, Types and Applications. Binomial Distribution and its Applications Poisson Distribution and its Applications Normal Distribution and its Applications Exponential Distribution and its ApplicationsShakehand with Life “Quality: A parameter of customer satisfaction.” Page 3www.shakehandwithlife.blogspot.com
    • Feedback Given by Management Professionals Very good performance given by Mr. Sharma , I am highly satisfied with the methodology of his teaching..................Shiv Parsad Mr. Sharma always well prepared before his course of work. Teaching Methodology is extremely good............Anil Kumar Mr. Sharma is very enthusiastic and affect me intellectually. He has excellent skill of encouragement in goal achievement...............Saurabh Mr. Sharma has given his best. We have learnt a lot under his teaching........................Swati Gupta Mr. Sharma is a very experienced person, his knowledge about his subject is great. His teaching skills are very effective...........Deepika Malhotra Communication skill of Mr. Sharma is very good. He explained the problem in very easy way. His knowledge about the subject is very good....................Nidhi Gupta In My view Mr.Sharma has taken up a very effective and efficient class. It really helps me a lot in every field like communication, leadership , I really thanks a lot to him for this..............Manan Madan Success never comes to knock the door and breakthrough can creates anytime for any success, this class is breakthrough for me......Manish Difficulty we face in the class is solved by Mr. Sharma in a very easy way ..............Deepak Wadhwa Provided good quality of study material. Pattern of teaching is very interesting and motivating, it will surly help me my personal as well as my professional life..........................Shelly Sharma He is a good teacher. I feel motivated by him in studying this subject. Activity and examples given by him are very good and helpful in understanding the subject...............Jyoti Nagpal Mr. Sharma as a Trainer/Teacher is very good and has ability to explain the topic with suitable examples. He has good communication skills and co-ordination with student..................Sushma Kumari I appreciate one thing that he creates a very good environment, everyone is involved and forced to think in the class whether he/she is present in the class mentally or not.................Seema KhannaShakehand with Life “Quality: A parameter of customer satisfaction.” Page 4www.shakehandwithlife.blogspot.com
    • Communication and experience of trainer is very good. I hope this kind of teacher should be provided for the rest of the subjects. I recommend him for my juniors and the friends in other institutes.........Binay Kumar Shukla Mr. Sharma is a very good and helpful teacher. His style of teaching is unique and takes students into confidence very easily. It enhances personality of an individual which is very helpful in any organization now a days..........................Praveen Mittal Very Energetic and motivated person. Know how to drive a person for his goal achievement. Efficient co- ordination. Team oriented and expert in his subject.....................................Vijay Shakher Arora Mr. Sharma has given his 100%. He tried to convey the message in a very appropriate manner with high level of technical (Audio-Visual) and traditional method. His capacity is remarkable to define the particular topic..............................Faeem AhmadTopper ‘s Words Teaching methodology is very comprehensive and helpful in understanding and cracking the problem in a systematic way..............Rahul Arora Rahul Arora is a Quality Engineer in a Genset Manufacturing organization. He scored 79 Marks in his QT examination held in July 2010.A good Trainer. Taught as a friend. Taught according to the mental capacity ofthe students and grown them up to the mark. Overall satisfied with the way andknowledge for the average students like us..............Prakash ChandraPrakash is working as Quality professional in a Software company . He Scored78 Marks in his QT examination held in July 2009. I like the teaching skill of Mr. Sharma. He enn courages me a lot and challenged me intellectually to achieve my goals...........Arti Mishra Arti Mishra working as teacher for Sr. Secondary classes. She scored 72 marks in her QT examination held in July 2010.Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 5www.shakehandwithlife.blogspot.com
    • Unit IQue. 1 A firm produces three products P, Q , and R requiring the mix-up of three materials M1 , M2 and M3 . Theper unit requirement for each material (in units) is as follows :Using Matrix notations find : (i) The total requirements of each material if the firm produces 100 units of each product. (ii) Total cost of production of each product if the per unit cost of material M1 , M2 and M3 is Rs. 5.00 , 10.00 and Rs. 5.00 respectively, and (iii) The total cost of production if the firm produces 200 units of each product.Solution : Given (i) Let B is column matrix of 100 units of each productTotal requirement of each material given by multiplication matrix A and B i.e. AB Or (ii) Let C be a column matrix which shows the unit cost of each material (M1 , M2 , M3)Multiplication Matrix A and C gives the total cost of production of each product (iii) Let a row matrix D, which shows 200 units of each product. Multiplication of Matrix D with Matrix AC will give the total cost of production when firm produce 200 units of each product.Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 6www.shakehandwithlife.blogspot.com
    • Que. 2 Matrix A and B give the daily sales and sale price of chocolates for a shopkeeper.Find the total revenue for four days.Solution : Total revenue will given by the multiplication of Matrix A with column Matrix BAB=AB= Unit IIQue. 3. Giving example explain the followingBar diagram , Multiple bar diagram, pie diagram and pictogramSolution:Bar Diagram : A Bar diagram is graph on which the data are represented in the form of bars. It consists of a number ofbars or rectangles on x-axis which are of uniform width. The length of the bars is proportional to the value itrepresents and are shown along y-axis. The width of rectangle does not convey any meaning. It is to be notedthat the width of the classes should be equal and in ascending order of magnitude. If the width of classes is notequal it should be made so by dividing its frequency equally.Example : Bar diagram for the following frequency distribution Marks 10-15 15-20 20-25 25-30 30-35 35-40 Frequency 5 12 22 18 10 8“A lifetime of happiness ! No man alive could bear it: it would be hell on earth.”Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 7www.shakehandwithlife.blogspot.com
    • Bar Diagram 25 22 20 18 Frequency 15 12 10 10 8 5 5 0 10-15 15-20 20-25 25-30 30-35 35-40 MarksMultiple Bar DiagramMultiple bar diagrams are diagrams are those diagrams which are used to compare two or more relatedvariables with respect to time or location or in other words these diagrams represent more than one type ofdata at a time. For every set of values, the bars of related variables are kept adjacent to each other. These barsare shaded or colored differently to distinguish between various variables. The method is illustrated in thefollowing example :Example : A multiple bar diagram chart of the production of wheat , rice and sugar from 1990 to 1994 (inmillion tons) Year 1990 1991 1992 1993 1994 Wheat 10 12 14 12 14 Rice 8 10 10.5 11 13 Sugar 7 7.5 9 8.5 8 16 Multiple Bar Diagram Wheat 14 14 14 13 Production in (Million Tons) Rice 12 12 12 Sugar 11 10.5 10 10 10 9 8.5 8 8 8 7.5 7 6 4 2 0 1990 1991 1992 1993 1994 YearShakehand with Life “Quality: A parameter of customer satisfaction.” Page 8www.shakehandwithlife.blogspot.com
    • Pie DiagramPie diagrams or Pie charts are used to expose the proportion of the individual items with reference to the total.As the areas of the sectors of a circle are directly proportional to their angles subtended at the centre, thus theangles of various sectors are calculated. The angle at the centre is 3600 which represents the aggregate. Thisangle of 3600 is divided into a number of small angles whose degrees will be proportional to the values ofcomponent. To draw a pie chart the following steps are taken: 1. First of all , find the fraction by dividing each frequency by the sum (total) of frequencies. 2. Multiply this fraction by 3600 . 3. Draw a circle and then draw the angles obtained by multiplying the fraction by 3600 at the centre if the circle.Example : Pie chart for the following data. Subject: English Maths Physics Chemistry Economics Commerce No. of Students : 45 60 20 30 10 15To draw the pie chart of the given data, we first calculate the angle at centre as shown in following table : No. of Students Subject Fraction of total Angle of centre (Frequency) English 45 Mathematics 60 Physics 20 Chemistry 30 Economics 10 Commerce 15 Total=180The pie chart is obtained by marking the angles obtained in the above table at the centre of the circle. Pie Chart Commerce, 15 Economics, 10 Chemistry, 30 English, 45 Physics, 20 Mathematics, 60Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 9www.shakehandwithlife.blogspot.com
    • Pictograms :Pictograms also known as pictographs, are very popularly used in presenting statistical data. Pictographs showdata in the form of pictures.For examples, data on scooters would be represented by pictures of scooters, data on milk diary by picture ofcows, data on population would be represented by pictures of men , data on milk would be represented by thebottles of milk and likeQue. 4 168 handloom factories have the following distribution of average number of workers in various incomegroups : 750-900 900-1100 1100-1400 1400-1800 1800-2400 40 32 25 28 42 Average no. of 8 12 8 8 4 workersFind the mean salary paid to the workers.Solution: To calculate the mean salary paid to the workers we have to proceed as below Average no. of Mid –Values (1) workers (M) (3) (4) 750-900 40 8 320 264000 900-1100 1000 32 12 384 384000 1100-1400 1250 26 8 208 260000 1400-1800 1600 28 8 224 358400 1800-2400 2100 42 4 168 352800 Unit -IIIQue. 5 Obtain the two lines of regression from the following data and estimate the blood pressure when age isfifty years: Age in Years 56 42 72 39 63 47 52 49 40 42 68 60 Blood Pressure 127 112 140 118 129 116 130 125 115 120 135 133Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 10www.shakehandwithlife.blogspot.com
    • Solution: Let Age represented by ‘x’ and Blood pressure is represented by ‘y’. Blood Pressure ( 56 127 7112 3136 16129 42 112 4704 1764 12544 72 140 10080 5184 19600 39 118 4602 1521 13924 63 129 8127 3969 16641 47 116 5452 2209 13456 52 130 6760 2704 16900 49 125 6125 2401 15625 40 115 4600 1600 13225 42 120 5040 1764 14400 68 135 9180 4624 18225 60 133 7980 3600 17689Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 11www.shakehandwithlife.blogspot.com
    • For estimating Blood pressure when age is 50, we will use regression equation (1) i.e. “y on x”Age (x) =50 put the value of x in equation (1)Therefore Blood pressure at the age of 50 is 123.2Que. 6 Estimate the trend values using the data given below by taking a four-yearly moving average:Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004Values 18 25 39 54 70 87 106 103 82 65 49 34 20 7Solution: Years Values Four- Yearly Moving Total Four Yearly -Moving Average - 1991 18 - 1992 25 - 1993 39 18+25+39+54=136 1994 54 25+39+54+70=188 1995 70 39+54+70+87=250 1996 87 54+70+87+106=317 1997 106 70+87+106+103=366 1998 103 87+106+103+82=378 1999 82 106+103+82+65=356 2000 65 103+82+65+49=299 2001 49 82+65+49+34=230 2002 34 65+49+34+20=168 2003 20 49+34+20+7=110 2004 7Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 12www.shakehandwithlife.blogspot.com
    • A graph of 4 yearly moving average using advance statistical software MINITAB is shown below 4 Yearly Moving Average Plot 120 Variable 106 A ctual 103 Fits 100 94.50 91.50 Mov ing A v erage 87 89.00 Length 4 82 79.25 80 74.75 70 65 62.50 Values 60 57.50 54 47.00 49 42.00 39 40 34.00 34 25 18 20 20 7 0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Year Unit –IVQue. 7(a) State and prove the theorems of probability.Solution:Addition Theorem :Addition theorem for Mutually Exclusive Events:“Addition theorem states that if A and B are two mutually exclusive events, then the probability of occurrenceof either event A or B is the sum of the individual probability of A and B.”Symbolically,Proof of the theorem: Let ‘n’ be the total number of exhaustive and equally likely cases of an experiment.Further let m1 and m2 be the number of cases favourable to the happening of the event A and B respectively.Then ,Since the events A and B are mutually exclusive, the total number of ways in which event A or B can happen is , thenShakehand with Life “Quality: A parameter of customer satisfaction.” Page 13www.shakehandwithlife.blogspot.com
    • Generalization: The theorem can be extended to three or more mutually exclusive events. If A, B and C are threemutually exclusive events, thenMultiplication TheoremMultiplication Theorem of probability is studied under two headings:Multiplication Theorem for Independent EventsStatement: It states that if A and B are two Independent events, then the probability of the simultaneousoccurrence of A and B is equal to the product of their Individual probabilities. Symbolically,Proof of the Theorem: Let m1 be the no. of cases favourable to the happening of the event A out of n1 exhaustiveand equally likely cases.Let m2 be the no. of cases favourable to the happening of the event of B out of n2 exhaustive and equally likelycases.Now the fundamental principal of counting, the no of cases favourable to the happening of the event AB is out ofGeneralization: The theorem can be extended to three or more independent events. If A B and C areindependent events, thenBayes’ TheoremNamed after British Mathematician Thomes Bayes (1763) also called Theorem of Inverse Probability.Statement of Bayes’ Theorem:Let E1 and E2 …….., En be ‘n’ mutually exclusive and exhaustive events with non-zero probabilities, of a randomexperiment. If A be any arbitrary event of sample space of the above experiment with P(A)>0 thenProof of the theorem: Consider the sample space given belowShakehand with Life “Quality: A parameter of customer satisfaction.” Page 14www.shakehandwithlife.blogspot.com
    • S A E1 E 2 E3………EnLet ‘S’ be the sample space of the random experimentNowNowRemarks: if n=2 thenQue. 7(b) Taking suitable example explain the baye’s theorem.Solution : Let an Insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers.The probability of accident is 0.01, 0.03, 0.15 respectively. One of the insured people meets an accidents . Tofind the probability that he is a scooter driver we can use the Baye’s theorem.Total No. of insured persons =2000+4000+6000=12000Let be the events that an insured person be scooter driver , car driver and truck driverrespectively. Let D be the event that insured person meets an accident.We haveConditional probabilitiesShakehand with Life “Quality: A parameter of customer satisfaction.” Page 15www.shakehandwithlife.blogspot.com
    • The events are mutually exclusive and exhaustive.By Bayes’ theorem,Que.8 A company has two plants to manufacture scooters. Plant I manufactures 70% of the scooters and plant IImanufactures 30%. At plant I, 80% scooters are rated standard quality and at plant II, 90% of the scooters arerated standard quality. A scooter is picked up at random and is found to be standard quality. What is the chancethat it comes from Plant I ?Solution : Let be the events that the selected scooter us manufactured by Plant I and Plant II. Let D bethe event that scooter is of standard quality.We haveConditional probabilitiesThe events are mutually exclusive and exhaustive.By Bayes’ theorem,“Experience is not what happens to a man ; it is what a man does with what happens to him.”Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 16www.shakehandwithlife.blogspot.com
    • Contact : Call me for telephonic support on Wednesday , Thursday , Friday , Saturday , Sunday at 7:00PM to 9:00PM. I request for your seriousness and honesty. Plz have patience if you hear “your call is on wait”. For home tuition and contact classes student and institute first send a request on my email id below mentioned. You can mail me at : sharma_ndr21@rediffmail.com narendersharma21@indiatimes.com You can find me at: http://www.facebook.com/profile.php?id=100000837976546 http://www.linkedin.com/profile/view?id=68376470&trk=tab_pro You can visit on my webpage to read the internationally acclaimed story “Statistics of Love” to understand basic statistics. www.shakehandwithlife.blogspot.comShakehand with Life “Quality: A parameter of customer satisfaction.” Page 17www.shakehandwithlife.blogspot.com
    • “Success can never lower its standard, you have to raise your standard to achieve it.” I wish for your dreams to be succeed. All the Best !Shakehand with Life “Quality: A parameter of customer satisfaction.” Page 18www.shakehandwithlife.blogspot.com