## Loyola College B.Sc. Commerce April 2011 Statistics For Management Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMMERCE & BUSIN. ADM.

FOURTH SEMESTER – APRIL 2011

# ST 4208 – STATISTICS FOR MANAGEMENT

Date : 05-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION A                                         (10 X 2 = 20 marks)

1. Define probability and give an example.
2. State addition theorem on probability.
3. State the Central Limit Theorem.
4. Explain the term standard error.
5. Define index number and discuss their importance.
6. Discuss any two steps in the construction of a cost of living index by the family budget method.
7. Distinguish between the control limits and tolerance limits.
8. Distinguish between np chart and p chart.
9. Define the term feasible solution.
10. What is meant by balanced and unbalanced transportation problem.

SECTION B                                          (5 X 8 = 40 Marks)

• State and prove Baye’s theorem.

• A sub-committee of 6 members is to be formed out of a group consisting of 7 men and 4 women calculate the probability that sub-committee will consist of.
1. a) exactly 2 women b) at least 2 women.
2. Two Urns contain respectively 10 white, 6 red and 9 black and 3 white 7 red and 15 black balls.

One ball is drawn from each Urn.  Find the probability that (i)  Both balls are red      (ii)  Both balls

are of the same colour.

14.If a random variable X follows a Poisson distribution such that P[ X = 2 ] = P[X=1].

Find P[X=0]. ( e -2  = 0.13534).

1. In a survey of 200 boys, of which 75 are intelligent, 40 of the intelligent boys have skilled fathers while 85 of the unintelligent  boys have unskilled fathers. Do these figures support the hypothesis that

skilled fathers have intelligent boys. Use chi-square – test of 5 % level.

1. From the following data of the whole sale prices of wheat for the ten years construct

Index numbers taking (a) 1979 as base and (b)by chain base method

 year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 Price of Wheat 50 60 62 65 70 78 82 84 88 90

1. The following table gives the number of defective items found in 20 successive samples of 100 items each

2    6   2   4   4   15   0   4   10   18   2   4   6   4   8   0   2   2   4   0

Comment whether the process is under control. Suggest suitable control limits for the future.

1. A company has 4 machine to be assigned to 4 of the 4 workers available for this purpose.

The expected production from each machine operated by each workers is given below.

WORKERS

 W1 W2 W3 W4 I 41 72 39 52 II 22 29 49 65 III 27 39 60 51 IV 45 50 48 52

MACHINE

Suggest optimal assignment of workers to machine.

SECTION   C                                   (2 X 20  =  40 Marks)

19.(a) A Company has four production sections viz. S1, S2, S3 and S4 , which contribute  30%, 20%, 28% and  22% of the total output. It was observed that those sections  respectively produced 1%, 2%, 3% and 4%   defective units. If a unit is selected at  random and found to be defective, what is the probability that  the units so selected has  come from either S1 or S4.?                                                            (10)

19.(b)The customer accounts of a certain departmental store have an average balance of Rs.120 and a standard deviation of Rs.40. Assuming that the account balances are normally distributed, find

• What proportion of accounts is over Rs.150?
• What proportion of accounts is between Rs.100 and Rs.150?

(iii)        What proportion of accounts is between Rs.60 and Rs.90 ?                                      (10)

1. (a) The sales manager of a large company conducted a sample survey in states A and B taking 400

Samples in each case. The results were as follow

State A               State B

Average sales             Rs.2500               Rs.2200

Standard Deviation      Rs.400                Rs.550

Test whether the average sales is the same in the two states. Test at 1% level.                                     (10)

20(b) The following table gives the fields of 15 samples of plot under three varieties of seed.

 A B C 20 18 25 21 20 28 23 17 22 16 15 28 20 25 32

Test using analysis of variance whether there is a significant difference in the average yield of seeds

21.(a) The following data show the values of sample mean (x) and the range (R) for ten samples of size 5 each       calculate the values for central line and control limits for mean chart and determine whether the process is    control.

 Sample 1 2 3 4 5 6 7 8 9 10 Mean 11.2 11.8 10.8 11.6 11 9.6 10.4 9.6 10.6 10.6 Range(R) 7 4 8 5 7 4 8 4 7 9

( For n = 5 , A2=0.577,D2 = 0, D4= 2.115)

21(b).Calculate Laspeyre’s Index number, Paasche’s price index number and Marshall-Edgeworth Index and how it satisfies Time reversal test and Factor reversal test.

 Commodity 1980 1981 Price (in Rs.) Quantity (in kgs.) Price (in Rs.) Quantity (in kgs.) A 20 15 30 10 B 30 18 40 15 C 10 20 45 10 D 15 25 25 5

22(a)Find the initial basic feasible solution by Vogel’s Approximation method.

Distribution Centers

 Plants D1 D2 D3 Supply P1 16 19 12 14 P2 22 13 19 16 P3 14 28 8 12 Demand 10 15 17

22(b) Solve the following game by graphical method.

Player A

a1      a2    a3      a4

b1     -2   5    6   -4

Player B

b2     4    -3     -1   6

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## Loyola College B.Com Corporate & Secretaryship April 2007 Statistics For Management Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 MS 09

BBA & B.Com. Corp.  DEGREE EXAMINATION

FOURTH SEMESTER – APRIL 2007

# ST 4203 – STATISTICS FOR MANAGEMENT

Date & Time: 19/04/2007 / 9:00 – 12:00          Dept. No.                                                     Max. : 100 Marks

SECTION A

Answer ALL questions.                                                                 (10 x 2 =20 marks)

1. Define equally likely events and give an example.
2. The mean of a Binomial distribution is 4 and variance is 3. Find P(X = 15).
3. What is the objective of statistical quality control?
4. Name some variable control charts.
5. State the addition theorem of probability.
6. What are index numbers? What do they measure?
7. State any two methods of constructing weighted index numbers.
8. State the minimax-maximin principle in game theory.
9. Find the value of the game:
 B1 B2 A1 0 2 A2 -1 4
1. What are the two types of errors in testing of hypothesis?

SECTION B

Answer any FIVE questions.                                                          (5 x 8 =40 marks)

1. An urn contains 6 white, 4 red and 9 blue balls. If 3 balls are drawn at random, find the probability that,
• 2 of the balls drawn are white, (ii) one is of each colour
• none is red, (iv) atleast one is white

1. For a Binomial distribution with parameters n = 5, p = 0.3, find the probabilities of getting, (i) atleast 3 successes,  (ii) atmost 3 successes

(iii) exactly 3 failures,  (iv) exactly 3 successes

1. Construct a control chart for C, ie., number of defects from the following data pertaining to the imperfections in 20 pieces of cloth of equal length in a certain make of polyester and infer whether the process is in a state of control: 2, 3, 5, 8, 12, 2, 3, 4, 6, 5, 6, 10, 4, 6, 5, 7, 4, 9, 7, 3.

1. Explain quality assurance, statistical process control, and types of control charts.

1. The following data relate to the prices and quantities of 5 commodities in the years 2005 and 2006. Construct the following index numbers for prices for the year 2006, taking 2005 as the base, (i) Laspeyre’s, (ii) Paasche’s, (iii) Fisher’s Ideal,

(iv) Bowleys.

 Commodities Base Year Current Year Quantity Price Quantity Price A 8 4 10 9 B 7 3 8 5 C 6 4 5 8 D 5 2 7 4

1. (i) Define Linear Programming.

(ii) A company has 3 operational departments (weaving, processing and packing) with capacity to produce 3 different types of clothes namely suitings, shirtings and woolens yielding profit of   Rs. 2, Rs. 4, and Rs. 3 per metre respectively. One metre suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly one metre of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minute in packing, while one metre of woolen requires 3 minutes in each department. In a week, total run time of each department is 60, 40 and 80 hours for weaving, processing and packing departments respectively. Formulate the LPP to find the product mix to maximize the profit.

1. Solve the following game graphically:

Player B

Player A

1. Set up an ANOVA table for the following per hectare yield (in 100 Kgs) for 3 varieties of rice, each grown in 4 plots:

 Variety of rice Plots of land R1 R2 R3 1 6 5 5 2 7 5 4 3 3 3 3 4 8 7 4

Test whether there is significant difference among the average yields in the 3 varieties of wheat, at 5 % level.

SECTION C

Answer any TWO questions.                                                        (2 x 20 =40 marks)

1. (i) Write down the probability distribution function of a Poisson random variable, and fit a poisson distribution to the following data: (Given e _ .05 = 0.61)
 X 0 1 2 3 4 Frequency 122 122 60 15 2

(ii) Students of a class were given an aptitude test. Their marks were found to be normally distributed with mean 60 and standard deviation 5. What percentage of the students scored:

• more than 60 marks, (b) less than 56 marks (c) between 45 and 65 marks. (12 + 8)

1. From the following data calculate the control limits for the mean and range control charts and also check if the process is in control. Measurements of the units are given in cms.
 S.No of Samples 1 2 3 4 5 6 7 8 9 10 50 51 50 48 46 55 45 50 47 56 55 50 53 53 50 51 48 56 53 53 52 53 48 50 44 56 53 54 49 55 49 50 52 51 48 47 48 53 52 54 54 46 47 53 47 51 51 57 54 52

U

N

I

T

S

 Commodity 2002 2003 2004 2005 2006 I 2 3 5 7 8 II 8 10 12 4 18 III 4 5 7 9 12
1. (i) Calculate fixed base index numbers and chain base index numbers for the following

(ii) Determine the least cost allocation of the available machines to 5 jobs.

 Jobs Machines A B C D E 1 25 29 31 42 37 2 22 19 35 18 26 3 39 38 26 20 33 4 34 27 28 40 32 5 24 42 36 23 45

(10 + 10)

1. There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.

 D E F G Supply A 6 8 8 5 30 B 5 11 9 7 40 C 8 9 7 13 50 Demand 35 28 32 25

Find out the solution for transporting the products at a minimum cost by using  (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best solution.

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## Loyola College B.Com April 2012 Statistics For Management Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Com., B.B.A., DEGREE EXAMINATION – COMM. & BUSI. ADMIN.

FOURTH SEMESTER – APRIL 2012

# ST 4208 – STATISTICS FOR MANAGEMENT

Date : 19-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

SECTION A

Answer ALL questions.                                                                                           (10 X 2 = 20 marks)

1. State addition theorem on probability.

1. Write Any four properties of normal distribution
2. Explain the term standard error.
3. State the assumptions made in analysis of variance.
4. Define index number and discuss their importance.
5. What is meant by Cost of Living Index Number?

1. What is statistical quality control? Point out its importance in the industrial world?
2. Distinguish between p chart and c chart.
3. Mention any two applications of linear programming.
4. What is balanced and unbalanced Transportation problem?

SECTION B

Answer any FIVE questions:                                                                      (5 X 8 = 40 Marks)

11.State and prove Boole’s  inequality.

1. Five men in a company of 20 are graduates. If 3 men are picked out from this 20 persons at random,

what  is the probability that (i) all are graduates (ii) at least one is graduate?

1. The following table gives the data on the hardness of wood stored outside and inside the room.

 Outside Inside Sample Size 40 110 Mean 117 132 Sum of squares of deviation from mean 8655 27244

Test whether the hardness is effected by weathering at 5% level

1. An IQ test was administered to 5 persons before and after they were trained. The results are given below:
 Candidates I II III IV V IQ before training 110 120 123 132 125 IQ after training 120 118 125 136 121

Test whether there is any change in IQ after the training programme. Use 5% level of  significance.

1. From the following data of wholesale prices of wheat construct Chain base index taking 1993 as origin.
 Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Price(in Rs.) per quintal 50 60 62 65 70 78 82 84 88 90

1. The following table gives the number of defective items found in 20 successive samples of 100 items each

2    6   2   4   4   15   0   4   10   18   2   4   6   4   8   0   2   2   4   0

Comment whether the process is under control. Suggest suitable control limits for the future.

1. A company produces two types of pens say A and B. Pen A is a superior quality and pen B is a lower quality. Profit on pen A and pen B are Rs.5 and Rs.3 per pen respectively. Raw materials required for each Pen A are twice as that of pen B the supply of raw materials is sufficient only 1000 pens of per day. Pen A requires a special clip of only 400 clips are available per day. For pen B only 700 clips are available per day. Find graphically the product mix so that the company can make maximum profit.

SECTION   C                                    (2 X 20  =  40 Marks)

1. (a) A factory manufacturing television has four units A, B, C and D. The units A, B, C and D manufactures 15%, 20%, 30%, and  35%, of the total output respectively. It was found that out of their outputs 1%, 2%, 2% and 3% are defective. A television is chosen at random from the output and found to be defective. What is the probability that, it came from unit D?                                                                       (10)

19.(b) Out of 8000 graduates in a town, 800 are females and out of 1600 graduates employees 120 are female.   Use Chi-square  test at 5%   level to determine if any distinction is made in appointment on the  basis of sex.                                                                                                                                 (10)

1. Develop the Two- way ANOVA  for the following data:

Treatment

 A B C D I 3 4 6 6 II 6 4 5 3 III 6 6 4 7

(20)

21.(a) The number of defects detected in 20 items are given below

Item No       :  1   2    3    4     5    6   7    8     9    10    11     12    13    14   15   16   17   18  19    20

No. of defects         :  2    0   4   1      0     0   8     1    2     0      6        0     2      1    0      3    2      1   0    2

Test whether the process is under control. Device a suitable scheme for future.                 (10)

21(b)Using the following data compute Fisher’s Ideal price and Quantity Index numbers for the current

year and also verify factor reversal test.

 COMMODITY Base year price Current Year Price Base year quantity Current Year quantity A 8 12 6 4 B 10 12 8 8 C 14 18 4 4 D 4 2 6 10 E 10 14 10 8

(10)

22(a). A company has 4 machine to be assigned to 4 of the 4 workers available for this purpose.

The expected production from each machine operated by each workers is given below.

WORKERS

 W1 W2 W3 W4 I 41 72 39 52 II 22 29 49 65 III 27 39 60 51 IV 45 50 48 52

MACHINE

Suggest optimal assignment of workers to machine.                                                                     (10)

22(b).Solve the following Transportation problem by using Vogel’s Approximation Method.

 D1 D2 D3 D4 D5 Availability A1 5 7 10 5 3 5 A2 8 6 9 12 14 10 A3 10 9 8 10 15 10 Demand 3 3 10 5 4

(10)

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Com.,B.B.A. DEGREE EXAMINATION – CORPORATE & BUS.ADMIN.

# NO 17

FOURTH SEMESTER – APRIL 2008

# ST 4208 / 4203 – STATISTICS FOR MANAGEMENT

Date : 24/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer ALL questions.                                                                       (10 x 2 =20 marks)

1. Define a random experiment and give an example.
2. A random experiment has the following probability function as follows, find E(X).

 X -1 0 1 P(X) 0.2 0.3 0.5

1. Differentiate between statistics and parameters.
2. What are the assumptions of analysis of variance test?
3. Define index numbers.
4. Name any 2 methods of constructing unweighted index numbers.
5. What are variable control charts? Name them.
6. For a quality control process, the mean is 0.5230 cm and standard deviation is 0.0032 cm. Calculate 3σ upper and lower control limits, if the sample size is 4.
7. Define a Linear Programming Problem.

B

1. Solve the following game:     A

SECTION B

Answer any FIVE questions.                                                               (5 x 8 =40 marks)

1. Aakash can solve 3 problems out of 5, Deepak can solve 2 out of 5 and Godfrey can solve 3 out of 4.What is the probability that:
• The problem will be solved
• Only two will solve the problem
1. The probability of an increase in demand of a particular product in the next year is 0.75. If this demand increase takes place, the probability that the sales will increase is 0.7. If there is no demand increase, the probability that the sales will increase is 0.5. Given that at the end of the year, the sale has risen, what is the probability that there was an increase in demand of the product?
2. A college conducts both day and evening classes intended to be identical. For a sample of 100 day students, the results was:  = 72.4 and σ = 14.8 and for a sample of 200 evening students, the exam results was:  = 73.9 and σ = 17.9. Are the two means statistically equal at 5% level of significance?
3. Edible oil is packed in tins holding 16 Kg each. The filling machine can maintain this but with a standard deviation of 0.5 Kg. Samples of 25 are taken from the production line. If the sample mean is 16.35 Kg, can we be 95 % sure that the sample has come from a population of 16 Kg tins?
4. Explain the uses of index numbers, and state the problems in the construction of index numbers.

1. The following table gives an inspection data on completed CD’s there were 2000 CD’s in 20 lots of 100 each. Draw a control chart for fraction defectives, and check if the process is in control.
 Lot No. 1 2 3 4 5 6 7 8 9 10 No. of defectives 5 10 12 8 6 5 6 3 3 5 Lot No. 11 12 13 14 15 16 17 18 19 20 No. of defectives 4 7 8 2 3 4 5 8 6 10

1. Solve the following Linear Programming Problem: Min z = 2 x + y subject to the constraints,  x ≤ 4, x + y ≥ 1, 5 x + 10 y ≤ 50, x, y ≥ 0.

1. Given the following data, determine the least cost allocation of the available machines M1, M2, M3, Mand M5,  to 5 jobs A, B, C, D and E.
 A B C D E M1 25 29 31 42 37 M2 22 19 35 18 26 M3 39 38 26 20 33 M4 34 27 28 40 32 M5 24 42 36 23 45

SECTION C

Answer any TWO questions.                                                               (2 x 20 =40 marks)

1. (i) The screws produced by a certain machine were checked by examining samples of 128. The following table shows the distribution of 128 samples according to the number of defective items they contained:
 No. of defectives 0 1 2 3 4 5 6 7 No. of samples 7 6 19 35 30 23 7 1

Fit a binomial distribution and find the expected frequencies if the chance of a screw being defective is ½. Also find the mean and variance of the distribution.

(ii) East-West airlines have the policy of employing women whose height is between 62 and 69 inches. If the height of women is approximately normally distributed with a mean of 64 inches and a standard deviation of 3 inches, out of the 1000 applications receives, find the number of applicants that would be (i) too tall (> 69), (ii) too short (< 62)

1. (i) A random sample is selected from each of 3 makes of ropes and their breaking strengths(in  pounds) are measured with the following results:
 I 70 72 75 80 83 II 100 110 108 112 113 120 107 III 60 65 57 84 87 73

Test whether the breaking strength of ropes differ significantly at 5% level of significance.

(ii) Construct Laspeyre’s, Paasche’s and Fisher’s Index numbers for the following data.

 2006 2007 Commodity Price Quantity Price Quantity A 2 8 4 6 B 5 10 6 5 C 4 14 5 10 D 2 19 2 13

1. Construct a control chart for mean and range for the following data on the basis of fuses, samples of 5 being taken every hour. Comment on whether the production seems to be under control.

 Sample Number 1 2 3 4 5 6 7 8 9 10 11 12 42 42 19 36 42 51 60 18 69 64 61 15 65 45 24 54 51 74 60 20 109 90 78 30 75 68 80 69 57 75 72 27 113 93 94 39 78 72 81 77 59 78 95 42 118 109 109 620 87 90 81 84 78 132 138 60 153 112 136 84

1. There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.

 D E F G Supply A 3 7 6 4 5 B 2 4 3 2 2 C 4 3 8 5 3 Demand 3 3 2 2

Find out the solution for transporting the products at a minimum cost by using  (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best solution.

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

 YB 17

FOURTH SEMESTER – April 2009

# ST 4208/ ST 4203 – STATISTICS FOR MANAGEMENT

Date & Time: 27/04/2009 / 9:00 – 12:00     Dept. No.                                                       Max. : 100 Marks

SECTION A                                   (10 X 2 = 20 Marks)

1. State the axioms of “Probability”.
2. Distinguish between Binomial and Poisson distribution.
3. State the Central Limit Theorem.
4. Write down the assumptions made in Analysis of Variance.
5. Define Index Number and discuss its importance.
6. What is meant by Cost of Living Index Number? What are its uses?
7. What is statistical Quality Control? Point out its importance in the Industrial World.
8. Distinguish between the Control Limits and Tolerance Limits.
9. Mentions any two applications of Linear Programming.
10. What is non-degeneracy problem in T.P.?

SECTION B                                    (5 X 8 = 40 Marks)

1. Define (i) Mutually Exclusive Events.

(ii)  Exhaustive Events.

(iii)  Independent Events.

1. Two Urns contain respectively 10 white, 6 red and 9 black and 3 white 7 red and

15 black balls.  One ball is drawn from each Urn.  Find the probability that

(i)  Both balls are red

(ii)  Both balls are of the same colour.

1. An automatic machine fills in tea in sealed tins with mean weight of tea 1 kg. and S.D. 1gm. A       random sample of 50 tins was examined and it was found that their mean weight was 999.50 gms.

Is the machine working properly?

1. The following are Index Numbers of Prices (1988 = 100)
 Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 Index 100 110 120 200 400 410 400 380 370 340

Calculate the chain base index.

1. The number of defects defected in 20 items are given below

Item No              :  1   2    3    4     5    6   7    8     9    10    11     12    13    14   15   16   17   18  19    20

No. of defects     :  2    0   4   1      0     0   8     1    2     0      6        0     2      1    0      3    2      1   0    2

Test whether the process is under control. Device a suitable scheme for future.

1. Explain the various types of control charts in use.
2. Solve the following unbalanced assignment problem of minimizing total time for

doing all the Jobs.

 JOBS J1 J2 J3 J4 J5 A 6 2 5 2 6 B 2 5 8 7 7 C 7 8 6 9 8 OPERATORS D 6 2 3 4 5 E 9 3 8 9 7 F 4 7 4 6 8
1. Out of 8000 graduates in a town, 800 are females and out of 1600 graduate employees

120 are female. Use chi-square  test at 5%   level, to determine if any distinction is made in appointment

on the  basis of sex.

SECTION   C                                   (2 X 20  =  40 Marks)

1. (a) Two boxes contain 12 white and 18 black and 15 white and 25 black balls respectively.  One  box was taken at random and a ball was taken from the same.  It is a black ball.  What is the probability that it is from the (i) first box (ii) second box ?

(b)  A machine produced 20 defective articles in a batch of 400.  After overhauling, it produced 10 defectives in a batch of 300.  Has the machine improved?                                          ( 10 +10 )

1. (a) Value of a Variety in two samples are given below:

 Sample I 5 6 8 1 12 4 3 9 6 10 Sample II 2 3 6 8 1 10 2 8 * *

Test the significance of the difference between the two population means, stating the assumptions involved.

20 (b)  The following table gives the fields of 15 samples of plot under three varieties of seed.

 A B C 20 18 25 21 20 28 23 17 22 16 15 28 20 25 32

Test using analysis of variance whether there is a significant difference in the average yield of seeds.                                                                                                           ( 10 +10 )

21 (a) The following figures give the number of defectives in 20 samples ,containing 2000 items

425, 430, 216, 341, 225, 322, 280, 306, 337, 305, 356, 402, 216, 264, 126, 409, 193, 280, 389, 350.

Calculate the values for central line and the control limits for p- chart.

(b)  Calculate Laspeyre`s , Paasche`s and Fishers Index Number for the data given below.

 Base Year Current Year Commodity Price Expenditure Price Expenditure A 5 50 6 72 B 7 84 10 80 C 10 80 12 96 D 4 20 5 30 E 8 56 8 64

( 10 +10 )

22 (a) Solve the following transportation problem by obtaining the initial solution

by VAM .

 Source Destination 1            2           3           4 Supply A   B   C 7            3           8           5   5            2           6          11   3            6           5           2 160   180   100 Demand 40         100       120       180 440

22 (b)  Solve the following game by using dominance rule:

 PLAYER B PLAYER B Y1 Y2 Y3 Y4 X1 19 6 7 5 X2 7 3 14 6 X3 12 8 18 4 X4 8 7 13 -1

( 10 +10 )

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