Gauhati University 2007 B.Com Quantitative Methods in Business(FIFTH ) - Question Paper

hours
The figures in the margin indicate full marks
for the ques.
ans ques. Nos. one and two and any 3 from the rest
1. ans the subsequent questions:
(a) Fill in the blank:
Sampling errors are not current in ___________________.
(b) select the accurate answer:
If the correlation ranging from 2 variables X and Y is negative, then the regression
coefficient of X on Y is
i) Positive
ii) Negative
iii) either positive or negative
iv) zero
(c) What is the range of Karl Pearson's correlation coefficient? 1
(d) choose the accurate option out of the provided ones: 2
Index number is a
i) measure of relative modifications
ii) special kind of avg.
iii) percentage relative
iv) All the above
(e) Mention 2 control charts for variables. 1
{f} elaborate the parameters of binomial distribution? 1
(g) describe feasible region associated with the solution of LP issues by graphical
method. 1
(h) State whether the subsequent statement is actual or False: 1
"Linear programming deals with issues involving only a single objective.”
2. ans any 5 of the subsequent questions: 5×5=25
a) Enumerate the different steps in sample survey.
b) State the multiplicative legal regulations of probability and illustrate it with an example.
c) If 5% of electric bulbs manufactured by a company are defective, use Poisson
distribution to obtain the probability that in a sample of 100 bulbs (i) none is
defective, (ii) five bulbs are defective. (Given e-5 = 0 . 007)
d) elaborate the characteristics of normal distribution?
e) explain in brief the issues of inventory management.
f) Write a note on Pareto's legal regulations of income distribution.
g) 2 persons X and Y were asked to rank seven various kinds of perfumes. The
ranks provided by them are as follows:
Perfumes: A B C D E F G
X: two one four three five seven 6
Y: one three 3 four five six 7
find rank correlation coefficient.
3. (a) A issue in Statistics is provided to 5 students A, B, C, D and E. Their
probabilities of solving it are ½,
, ¼, ¼ and 1/5 respectively. What is the probability
that at lowest 1 learner will be able to solve the problem? 7
(b) The distribution of monthly incomes of 500 workers is presumed to be normal with
mean of Rs 2,000 and standard deviation of Rs 200. Estimate the number of workers with
incomesi)
exceeding Rs 2,300 p.m.;
ii) ranging from Rs 1,800 and Rs 2,300 p.m.
What is the least income of the 25% workers in the highest income group?
[Given: Z = 0.67 1.00 1.50
Area = 0.25 0.3413 0.4322] 3+3+2=8
4. (a) find Karl Pearson's correlation coefficient for the subsequent bivariate
distribution: 7
x : one two three four five six seven eight 9
y : nine eight 10 12 11 13 14 16 15
(b) discuss the concept of regression. elaborate regression equations and regression
lines? Why there are usually 2 regression lines? When do they coincide?
3+2+2+ one =8
5. (a) elaborate type- I fault and type-II fault associated with tests of significance?
discuss the concept of level of significance. 5+2=7
(b) 2 sample poles of votes for 2 candidates A and B for a public office are taken,
one from among the residents of urban areas and the other from the residents of rural
areas. The outcomes are provided beneath. Use chi-square test to examine whether the nature of
the area is related to voting preference in this election:
Votes For A B Total
Rural 620 380 1000
Urban 550 450 1000
Total 1170 830 2000
Given: X 2
0.05 (1) = 3.84 8
6. (a) A company requires 10000 units of raw materials per annum. The cost per order is
estimated to be Rs 50. The storage cost is estimated to be Rs.5,00 per unit of avg.
inventory. What volume should be ordered so that the total cost is minimum? obtain also
the total minimum cost excluding the purchase cost. 5+3=8
(b) What is a control chart? discuss the background of 3cr control limits for a control
chart. 4+3=7
7. (a) explain the advantages and disadvantages of OR models. 7
(b) Solve the subsequent LPP by graphical method: 8
Maximize Z = 40x + 80y
subject to
2x+3y48
x 15
y 10
x, y0
8. (a) Solve by simplex method : 10
Maximize Z = 3x1+ 2x2 + 5X3
subject to
x1+2x2 +x3 430
3x1 + 2x3  460
x1+4x2 420
x1,x2,x3 0
(b) Write a note on the role and limitations of simulation. 5

Earning:   Approval pending.