LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Com.,B.B.A. DEGREE EXAMINATION – COMMERCE&BUS.ADMIN.&CORP.
SUPPLEMENTARY EXAMINATION – JUNE 2007
ST 4203 - STATISTICS FOR MANAGEMENT
Date & Time: 26/06/2007 / 1:00 - 4:00
Dept. No.
Max. : 100 Marks
SECTION A
Answer ALL questions.
(10 x 2 =20 marks)
1.
2.
3.
4.
5.
6.
7.
8.
9.
Define independent events and give an example.
Give some examples of binomial experiment.
Differentiate between assignable and chance causes in statistical quality control.
Name some attribute control charts.
State the uses of index numbers.
Differentiate between fixed base and chain base index numbers.
Define linear programming problem.
What are two person zero sum games?
Is the following game fair?
Player B
1 1
Player A 

1 1
10. What do you mean by level of significance?
SECTION B
Answer any FIVE questions.
(5 x 8 =40 marks)
11. A committee of 4 people is to be appointed from 3 officers of the production department, 4
officers from the purchase department, 2 officers of the sales department, and 1 chartered
accountant. Find the probability of forming the committee in the following manner.
(i)
There must be 1 from each category
(ii)
It should have at least 1 member from the purchase department
(iii)
The chartered accountant must be in the committee.
12. Let X be normally distributed with mean 8 and standard deviation 4. Then find:
≤ X ≤ 10), (ii) P( 10 ≤ X ≤ 15), (iii) P( X ≥15), (iv) P( X ≤ 5).
(i) P( 5
13. State the objective of statistical quality control and give the advantages of statistical quality
control.
14. From the following data of the wholesale prices (Rs. Per 10 Kg.) of corn for the ten years
construct index numbers taking, (i) 1996 as the base, (ii) by chain base method.
Year Price of Corn
1996
50
1997
60
1998
62
1999
65
2000
70
Year Price of Corn
2001
78
2002
82
2003
84
2004
88
2005
90
15. Solve the following transportation problem using Vogel’s Approximation method
A
B
C
Demand
D
6
5
8
35
E
8
11
9
28
F
8
9
7
32
G
5
7
13
25
Capacity
30
40
50
16. Obtain the optimal strategies for both persons and the value of the game for zero-sum two
person game whose payoff matrix is as follows:
Player B
1
 3 3 7 
Player A
 2 5 4  6


17. There are 4 salesmen, how should they be assigned to four zones A, B, C and D, so that the
total sales are maximized? Given the sales figures (in ‘000s Rs.) for each salesman-zone
combination.
A
Jinender 42
30
Pankaj
30
John
24
Mittal
B
35
25
25
20
C
28
20
20
16
D
21
15
15
12
18. A college conducts both day and evening classes intended to be identical. For a sample of
100 day students, the exam results was X = 72.4, σ = 14.8, and for a sample of 200 evening
students, the exam results was X = 73.9, σ = 17.9. Are the two means statistically equal at
10% level?
SECTION C
Answer any TWO questions.
(2 x 20 =40 marks)
19. (i) A company has 4 production sections 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 unit so selected has come from either S1 or S4.
(ii) Seven coins are tossed and the number of heads is noted. The experiment is
repeated 128 times and the following distribution is obtained:
No. of heads 0 1 2 3 4 5 6 7
7 6 19 35 30 23 7 1
Frequency
Fit a Binomial distribution assuming the coin is unbiased.
(8 +12)
2
20. 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.
1
42
65
75
78
87
2
42
45
68
72
90
3
19
24
80
81
81
4
36
54
69
77
84
Sample Number
5 6
7
42 51 60
51 74 60
57 75 72
59 78 95
78 132 138
8
18
20
27
42
60
9
69
109
113
118
153
10
64
90
93
109
112
11
61
78
94
109
136
12
15
30
39
620
84
21. (a) 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) Marshall-Edgeworth, (v) Bowleys.
Commodities
A
B
C
D
E
2005
2006
Quantity Price Quantity Price
125
15
150
13
100
12
80
15
150
8
125
10
200
10
250
8
80
6
60
9
(b) Compute the cost of living index number using both the Aggregate expenditure method
and family budget method, from the following information:
Commodity
Wheat
Rice
Pulses
Ghee
Sugar
Oil
Fuel
Clothing
Unit Consumption Price in
Price in
in base year
base year Current year
200
1
1.2
50
3
3.5
50
4
5
20
20
30
40
2.5
5
50
10
15
60
2
2.5
40
15
18
22. The New Electrical Co. manufactures two models of voltage stabilizers, Ordinary and
Automatic. All components of the stabilizers are purchased from outside sources and only
assembling and testing is carried out in the company. The assembling and testing time
required for the two models are 0.8 hours each for ordinary and 1.20 hours each for
automatic. Manufacturing capacity of 720 hours at present is available per week.
The market for the two models has been surveyed which suggests maximum weekly sale
of 600 units of ordinary and 400 units of automatic. Profit per unit for ordinary and automatic
models has been estimated at Rs.100 and Rs.150 respectively.
Find the optimal product mix using graphical method.
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