Reg. No. ________
Karunya University
(Karunya Institute of Technology and Sciences)
(Declared as Deemed to be University under Sec.3 of the UGC Act, 1956)
End Semester Examination – November/ December - 2012
Subject Title:
Subject Code:
STATISTICS AND NUMERICAL METHODS
09MA302
Time: 3 hours
Maximum Marks: 100
Answer ALL questions (5 x 20 = 100 Marks)
1.
Compulsory:
a.
b.
c.
2.
a.
b.
3.
a.
b.
4.
a.
b.
c.
Explain the meaning and significance of the concept of correlation. How is the coefficient
of correlation interpreted?
(4)
Define regression coefficient and write down any two properties.
(4)
The following measurements show the respective heights in inches of ten fathers and their
eldest sons.
(12)
Father(X) : 67 63 66 71 69 65 62 70 61 72
Son (Y) : 68 66 65 70 69 67 64 71 60 63
i. Find the regression line of son’s height on father’s height.
ii. Estimate the height of son for the given height of father as 70 inches.
iii. Find the regression line X on Y.
iv. At what point the two lines of regression intersect?
What is meant by classification? Discuss the different modes of classification.
(8)
The internal marks obtained in statistics and numerical methods by 100 students of a
university are as follows:
Marks
: 0-5
5-10
10-15 15-20 20-25 25-30 30-35 35-40
No. of Students : 4
6
10
10
25
22
18
5
Draw a cumulative frequency curve and hence find the median. Also verify the median
algebraically.
(12)
(OR)
What is coefficient of variation and its importance?
(8)
Compute standard deviation from the following data.
Age under
: 10
20
30
40
50
60
70
80
No. of persons dying : 15
30
53
75
100
110
115
125
(12)
State Bayes’ theorem.
(4)
Assume that a factory has two machines. Past records show that machine 1 produces 30%
of the items of output and machine 2 produces 70% of the items. Further, 5% of the items
produced by machine 1 were defective and only 1% produced by machine 2 were
defective. If a defective item is drawn at random, what is the probability that the defective
item was produced by machine 1 or machine 2?
(8)
A multiple-choice test consists of 8 questions with 3 answers to each question of which
only one is correct. A student answers each question by rolling balanced dice and checking
the first answer is he gets 1 or 2, the second answer if he gets 3 or 4 and the third answer is
he gets 5 or 6. To get a distinction, the student must secure at least 75% correct answers. If
there is no negative marking, what is the probability that the student secures a distinction?
(8)
(OR)
[P.T.O]
5.
a.
b.
c.
6.
a.
b.
7.
a.
b.
8.
a.
b.
9.
a.
b.
The probabilities of A, B and C becoming managers of a company are 4/9, 2/9 and 1/3
respectively. The probabilities that the bonus scheme will be introduced if A, B and C
becomes managers are 3/10, 1/2 and 4/5 respectively. Find the probability that the bonus
scheme will be introduced.
(4)
A vendor can purchase the newspapers at a special concessional rate of 25 paise per copy
against the selling price of 40 paise. Any unsold copies are, however a dead loss. A vendor
has estimated the following probability distribution for the number of copies demanded.
No. of copies
:
15
16
17
18
19
20
Probability
:
0.04
0.19
0.33
0.26
0.11
0.07
How many copies should be ordered so that his expected profit will be maximum? (8)
A company has installed 1000 electric bulbs in a corporation. If these bulbs have an
average life of 1000 burning hours with a standard deviation of 200 hours, assuming
normality, what number of bulbs might be expected to fail
i.
in the first 800 burning hours
ii. between 800 and 1200 burning hours. [P(0<z<1)=0.3413].
(8)
Solve the equation log x = cos x to five decimals by Newton-Raphson Method.
(10)
Solve the following by Gauss-Seidel method and correct to four decimal places. (10)
a+b+54c = 110, 27a+6b-c = 85, 6a+15b+2c=72.
(OR)
Discuss Bisection Method for solving an algebraic equation.
(8)
Apply Gauss-Jordan method to find the solution of the following system of equations.
10a+b+c=12, 2a+10b+c=13, a+b+5c=7.
(12)
Find the derivative of f(x) at x=0.4 from the following data by applying Newton’s
backward formula.
(10)
x :
0.1
0.2
0.3
0.4
f(x) :
1.10517
1.22140
1.34986
1.49182
Given dy/dx= (y-x)/(y+x), with the initial condition y(0)=1. Find y, when x=0.1 by
breaking up the interval into five steps.
(10)
(OR)
Discuss the Trapezoidal rule for evaluating a definite integral.
(8)
Use Runge Kutta method of fourth order to approximate y, when x = 0.3 given
dy/dx= -(xy2 +y), y(0)=1 by taking h=0.1.
(12)