LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Com., B.B.A. DEGREE EXAMINATION – CORPORAT.SECR. & BUS. ADMIN.
SUPPLEMENTARY EXAMINATION – JUNE 2009
ST 4208 - STATISTICS FOR MANAGEMENT
Date & Time: 25/06/2009 / 10:00 - 1:00 Dept. No.
SECTION A
Answer ALL questions.
Max. : 100 Marks
(10 X 2 = 20 marks)
1. Define probability and give an example.
2. Write any four properties of normal distribution.
3. Define type I – error and type – II error.
4. Explain the term standard error
5. What are index numbers? What are their uses ?
6. Discuss the steps in the construction of a cost of living index by the family budget method
7. Explain the various types of control chart.
8. State the advantages and disadvantage of statistical quality control.
9. Define the term feasible solution.
10. Write the steps of the Hungarian method for assignment problem.
SECTION B
(5 X 8 = 40 Marks)
Answer any FIVE questions
11. State addition and multiplication theorems on probability. Illustrate them by means of
an example
12. If 3% of the electric bulbs manufactured by a company are defective, find the
probability that in a sample of 100 bulbs, exactly five bulbs are defective (e-3 = 0.0498)
13. A sample of 400 male student is found to have a mean height of 171.38 cms. Can it be
reasonably regarded as a sample from a large population with mean height 171.17 cm
and standard deviation 3.30 cm?
14. 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
Price
Wheat
1988
50
1989
60
1990
62
1991
65
1992
70
1993
78
1994
82
1995
84
1996
88
1997
90
15. You are given below the values of sample mean(X) and the range (R) for ten samples of size 5
each. Draw mean and range charts and comment on the state of control of the process.
Sample No: 1
X: 43
R: 5
2
49
6
3
37
5
4
44
7
5
45
7
6
37
4
7
51
8
8
46
6
16. Distinguish between np-chart and c- chart
1
9
43
4
10
47
6
17.Solve the following transportation problem by VAM method.
Destination
Source
A
D1
3
D2
5
D3
8
D4 D5
9
11
Supply
20
B
5
4
10
7
10
40
C
2
5
8
7
5
30
Demand
10
15
25
30
40
18. Two groups of 100 people each were taken for testing the use of a vaccine,15 persons
contracted the disease out of the inoculated persons, while 25 contracted the disease
in the other group. Test the efficiency of the vaccine using chi-square test at 5% level.
SECTION C
(2 X 20 = 40 Marks)
Answer any TWO questions
19 (a) Each of six urns contains black and white balls; one has eight white and 4 black
balls; two have six 6 white and 6 black balls and three have 4 white and 8 black
an urn is drawn at random, and 3 balls are drawn without replacement from that urn
two of the three are white and the other is black. What is the probability that the urn
drawn contained 4 white and 8 black balls?
19(b) If 10% of the screws produced by an automatic machines are defectives, find the probability
that of 20 screws selected at random there are (i) exactly two defectives
(ii)at the most three defectives (iii) at least two defectives.
(10 +10 )
20(a) A company arranged an intensive training course for its team of salesmen. A random
Sample of 10 salesmen was selected and the value ( in 000) of their sales made in
the weeks immediately before and after the course are shown in the following table
Salesman
1
2
3
4
5
6
7
Sales before 12
23 5
18
10
21
19
Sales after
18
22 15 21
13
22
17
Test whether there is evidence of an increase in mean scale
8
15
19
9
8
12
10
14
16
20 (b) There are three main brands of a certain powder. A set of 120 sample values is examined and found
to be allocated
among four groups ( A,B, C and D ) and three brands ( I ,
II, III) as shown
here under
Brands
Groups
I
II
II
A B
0
4
5
8
18 19
C D
8 15
13 6
11 13
Is there any significant difference in brands preference? Answer at 5% level.
(10 +10 )
2
21(a) The following table gives the number of error of alignment observed at final inspection of a certain
method of bus. Prepare a c-chat and comment on it
Bus No
No.of allignment
Defects
1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010
4
6
10
8
7
12
9
5
7
3
4
1011 1012 1013
1014 1015
1016 1017
1018 1019
1020
8
6
10
16
6
12
3
4
2
1
21.(b)Using the following data, construct Fisher’s Ideal Index and show how it satisfies factor Reversal
test and Time Reversal test
Commodity Base year
Current
Base year
Current Year
Price
Year Price
Quantity
Quantity
A
B
C
D
E
6
2
4
10
8
10
2
6
12
12
50
100
60
50
40
56
120
60
24
36
(10 +10 )
22 (a) A company has 4 machine to be assigned to 4 of the 5 workers available for this purpose.
The expected production from each machine operated by each workers is given below.
WORKERS
MACHINE
I
II
III
IV
W1
40
48
49
30
W2
46
32
36
46
W3
48
36
41
49
W4
36
29
38
44
W5
48
44
45
47
Suggest optimal assignment of workers to machine.
22 (b)Reduce the following game by dominance and find the game value
Player B
I
II
III
IV
I
3
3
4
0
Player
A
II
2
4
2
4
III
4
2
4
0
IV
0
4
0
8
(10 +10 )
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