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Loyola College B.B.A. Business Administration April 2008 Statistics For Management Question Paper PDF Download

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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, M4  and 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 B.B.A. Business Administration April 2009 Statistics For Management Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.B.A DEGREE EXAMINATION – BUSINESS ADMINISTRATION

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)

     Answer ALL questions.

 

  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)

 

     Answer any FIVE questions

  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)

Answer any TWO questions

  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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