Thapar University 2006 M.C.A Research Methodology - Question Paper

Thapar Institute of Engineering & Technology
MCA (2ndYear)
Final Term exam
MA501 (Research Methodology)



School of Mathematics & Computer Applications End Semester Examination (11/12/2006)

MA-501 Research Methodology-Max Marks: 45    Time: 3 Hours

Note: Attempt any FIVE questions.

Use of Statistical tables is allowed.

Write your tutorial group on top of first page of answer sheet.

Evaluated answer sheets will be shown on 15 December 2006 (Friday), at 2:30 P.M. in room B-210.

4. (a) The distribution function of a random variable X is given below. F(x)=0 , * < 0

= y , 0 s x < 1 , 1 x<2

= 1 ,x3

Find the values of (i) P(X>l/2) (ii) P (2<X< 4) (iii) P(X=1).    3

(b)    A random variable X has the following probability distribution

x :    0 1 2 3 4 5 6 7

p(x):    0 k 2k 2k 3k k¹ 2k² 7k²+k

Find the values of (i) k (ii) E (X).    3

(c)    Gauges are used to reject all components where a certain dimension is not within the specifications 1.50 d. It is known that this measurement is normally distributed with mean 1.50 and standard deviation 0.2. Determine the value d such that the specifications cover 98% of the measurements.    3

5 (a) Define Poisson distribution and derive its mean.    2

(b)    A car firm has two cars, which it hires out day by day. The number of demands for a car on each day follows Poisson distribution with mean 1.5. Calculate

(i)    the proportions of days on which neither car is used, and

(ii)    the proportions of days on which some demand is refused.    3

(c)    To investigate the collapse of the roof of a building, a testing laboratory is given all the available bolts that connected the steel structure at 3 different positions on the roof. The process required to shear each of these bolts are as follows:

Position 1 : 90 82 79 98 83 91 Position 2: 105 89 93 104 89 95 86 Position 3: 83 89 80 94

Perform an analysis of variance to test whether the differences among the sample means at the three positions are significant.    4

6 (a) An industrial safety' program was recently instituted in the computer chip industry¹. The average weekly loss in the man-hours due to accident in 10 similar plants both before and after the program is as follows:

Plant 1 2 3 4 5 6 7 8 9 10 Before 30.5 18.5 24.5 32 16 15 23.5 25.5 28 18 After 23 21 22 28.5 14.5 15.5 24.5 21 23.5 16.5

Determine whether the safety program has been proven to be effective.    4

(b) The following table gives the level of education and marriage adjustment score for a sample of married women. Can you conclude from the above that higher the level of education, greater is

		Marriage	-Adjustment	score
level of education	very low	low	high	very high
College	24	97	62	58
High school	22	28	30	41
Middle School	32	10	11	20

1

   (a) Give the axiomatic definition of probability and derive P(A) + P{A) = 1.    2

(b)    There arc three machines I, II and III producing 3000, 2500 and 4500 bullets per hour respectively. These machines are known to produce 1%, 1.2% and .2% defective bullets respectively. One bullet is taken at random from an hours production of the three machines.

(i)    What is the probability that this bullet is defective?

(ii)    The drawn bullet is found to be defective, what is the probability that this was produced by machine II?    4

(c)    A bag contains 50 tickets numbered 1 to 50. Three tickets are drawn at random from the bag. What is the probability that the numbers on the selected tickets are in arithmetic progression?

3

Attachment: thapar-university-2006-m-c-a--26288-1.pdf

Earning:   Approval pending.