SVKM’s NMIMS UNIVERSITY
SCHOOL OF DISTANCE LEARNING
COURSE:
SUBJECT:
DATE:
TIME:
ADSCM/ADITM/ADBFM/PGDFM/PGDHRM/PGDMM
Quantitative Analysis for Managerial Applications
4-06-2008
MARKS: 100
3 P.M TO 6 P.M
 Attempt any five questions.
 All questions carry equal marks.
 Use of calculator is permitted.
Q.1
a) State the characteristics of Statistical Data.
b)
 1 3 2 


Explain the term linear function and step function. A   4 0 6  Find the adjoint of the
 5 7 3


matrixA.
c) What are the various measures of central tendency? Find the mean and mode for the following data: :
12,15,17,17,10,5,9,23,15
d) Obtain an equation of trend line by method of least squares for the data given below:
Year
1991
1992
1993
1994
1995
1996
1997
1998
Production 21
24
32
40
38
49
57
60
Q.2
a) A truck manufacturing company produces 400 trucks during the first year. The production of truck
was 700 in the 5th year. If the increase in production per year is constant, find the increase in the
production in each year. What will be the level of the output for the 12th year?
b) Solve by using matrices: 2x-3y+3z = 1; 2x+2y +3z = 2 and 3x -2y +2z =3
c) A portfolio Consultant firm has three advisors A, B, C to advise their clients for investments in the
secondary market. In a week the numbers of clients who take their advice and invest are 200, 180 and
120 respectively. ‘A’ being highly experienced has a reputation that 90% of clients following his advice
are benefited. The corresponding figures for B and C are 80% and 75% respectively. At the end of a
week, a client was selected at random and was found that he did not benefit from the advice. Find the
probability that B advised him
d) Calculate the Bowley’s Coefficient of Skew ness from the following data:
Monthly
1000 &
Below600
600-700
700-800
800-900
900-1000
wages
above
No. of
10
25
45
20
15
5
workers
Q.3
a) Explain the steps involved in Hypothesis testing. What do you mean by type I and type II errors in
hypothesis testing?
b) The daily profit ( in Rs.) of 100 shops are distributed as follows:
Profit per
up to 100
up to 200
up to 300
up to 400
up to 500
up to 600
shop
No. of
12
30
55
85
94
100
shops
Prepare the frequency distribution and draw histogram.
…..page-1
c) State the merits and limitations of Rank correlation coefficient. Find the same for the data given
below:
Marks
in
12
18
32
18
25
24
25
40
38
22
Maths
Marks
in
16
15
28
16
24
22
28
36
34
19
Stats.
d) In a certain lottery, one prize of Rs. 1000/- 3 prizes of Rs.500/- each, 5 prizes of Rs.100/- each and 10
prizes of Rs.50/- each are to be awarded to 19 tickets drawn from the total number of 10000 tickets sold
at a prize of Re.1/- ticket. Find the expected net gain, to a person buying a particular ticket.
X
1000
500
100
50
P(X) 1/10000
3/10000
5/100000
10/10000
Q.4
a) Compute mean and standard deviation for the following data.
Class
0-30
30-60
60-90
90-120
120-150
150-180
Freq.
8
15
17
20
11
9
b) A firm has revenue function given by R =8x where x is the output. The production cost is
C = 150000 + 60(x/900) 2 . Find the total profit function and the number of units to be sold to get the
maximum profit.
c) State the properties of probability density function of a continuous variable. Suppose the probability
density function of different weights of a “1Kg tea pack” of a company is given by:
f(x) = 100( x- 1) for -1≤ x ≤ 1.1
= 0 otherwise. Verify if it is a valid probability density function.
2
d)
 x 9 
1
1 

x 3
 3 
Evaluate: lim 
 and lim  2
x 1 x  x  2
x 3 

x 1 



Q.5
a) f(x) = 2x2 – 5x +4 , for what value of x if 2 f(x) = f(2x)
b) Future technologies ltd manufactures high resolution telescopes. The management wants its products to
have variation of less than two standard deviation in resolution, while focusing on objects which are
beyond 500 light years. When they tested their newly manufactured telescope for 30 times, to focus on
an object 500 light years away, they found that the sample standard deviation to be 1.46. State the
hypothesis and test it at 1% level of significance. Can the management accept to sell this product?
c) Write a note on time series analysis.
d) Write a note on forecasting for medium and short term decisions.
Q.6
a) Write a note on forecast control.
b) Compute the Karl Pearson’s coefficient of correlation:for the following data:
X
5
10
5
11
12
4
3
2
7
1
Y
1
6
2
8
5
1
4
6
5
2
c) The probability that A can solve a problem in mathematics is 4/5, that B can solve is 2/3 and that C
can solve is 3/7. If all of them try independently, find the probability that the problem will be solved.
d) Compare mean, median and mode.
…..page-2
Q.7
a) Determine the nature of the roots: i) x2 +3x +9/4 = 0, ii) 8x2 – 19x +8= 0
b) In a certain factory turning out optical lenses there is small chance of 1/500 for any lens to be
defective. The lenses are supplied in packets of 10. Use Poisson distribution to calculate the
approximate number of packets containing a) no defective, b)1 defective, c) 2 defective lenses in a
consignment of 20000 packets
c) Plot a histogram and a frequency polygon from the following data:
Marks
0-20
20-40
40-60
60-80
80-100
No. of Students
8
12
15
12
3
d) Explain the binomial distribution. The incidence of a certain disease is such that on an average 30% of
workers suffer from it. If 10 workers are selected at random, find the probability that exactly two
workers suffer from the disease.
Q.8
a)
b)
c)
d)
What is normal distribution? State its characteristics?
Solve by Cramer’s Rule: 2x-3y +z = 7; 2x+y-z =1 and 4y +3z = -11
Write a note on sampling.
The regression equation of Y on X is given by 8x – 10y +66 =0 and that of X on Y is 40x – 18y =214.
Find the two regression coefficients and the coefficient of correlation.
Q.9
a) A quality control engineer at Zen Automobiles wants to check the variability in the number of defects
in the cars coming from two assembly lines A and B . When he collected the data it was as shown
below :
Assembly line A
Assembly Line B
Mean
10
11
Variance
9
25
Sample size
20
16
Can he conclude that the assembly line B has more variability than line A?
 1 0
3 2
2x  y  
 and y = 
 Find x and y.
 3 2 
1 4
c) Plot the less than and more than Ogives for the data given below:
Income(Rs.)
10-20
20-30
30-40
40-50
50-60
No. of
90
340
400
240
140
families
d) Write a note on various non-probability sampling methods.
b)
60-70
70-80
40
30
…..page-3
Q.10
a) From the prices of shares of X and Y given below, state which share is more stable in value.
X
55
54
52
53
56
58
52
50
51
Y
108
107
105
105
106
107
104
103
104
49
101
b) A tyre company wants to test the stress of tyres. The tyres should withstand a minimum load of
80000Kgs, but excess load would burst the tyres. From the past experience, it is known that the
standard deviation of the load is 4000Kgs. A sample of 100 tyres was selected and tests were carried
on them. The result showed that the mean stress capacity of the sample is 79600Kgs. If the supplier
uses a level of significance of 0.05 in testing, do the tyres meet stress requirements?
c) Deseasonalize the data
Production (in tonnes)
Year
Quarter I
Quarter II
Quarter III
Quarter IV
1983
5
1
10
17
1984
7
1
10
16
1985
9
3
8
18
1986
5
2
15
19
d) Darjeeling Tea has developed a new blend of tea, Good Health having a superior taste and aroma than
the existing brands. It wants to test market the new product before launching it nation wide. It chooses
four cities and launches the product in these cities. After a month of launch, they surveyed the
individuals in these cities to find whether they liked this brand or not. The result of the survey is as
follows:
Delhi
Mumbai
Kolkata
Chennai
Total
No. of people
71
75
58
79
283
who liked
Good Health
No. of people
29
45
32
31
137
who didn’t
like Good
Health
Total
100
120
90
110
420
The manager of Darjeeling Tea wants to know whether the proportion of people who like the new
brand of tea, Good Health is same in all the four cities at a significance level of 10%? He uses X 2
distribution , what is his conclusion?
--------------------------……….page-4