B.E. (Civil)
STATISTICAL ANALYSIS & COMPUTATIONAL METHODS IN
CIVIL ENGINEERING
(2008 Pattern) (Elective – IV) (Sem. – II)
Time :3 Hours] [Max. Marks :100
Instructions to the candidates:
1) Answer any 3 questions from each section.
2) Answer 3 questions from Section 1 and 3 questions from Section – II.
3) Answers to the two sections should be written in separate answer books.
4) Neat diagrams must be drawn wherever necessary.
5) Pigures to the right indicate full marks.
6) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed.
7) Assume suitable data, if necessary.
SECTION – I
QI) a) Explain the role of statistics in engineering applications. [3]
b) Write an expression for coefficient of skewness and coefficient of Kurtosis and state what these coefficients indicate. [5]
c) The following table gives the S0_{2} concentration in ppm in the ambient air observed at a monitoring station. Determine the mean, median, mode and standard deviation for this data. [8]
Sr.No 
l 
2 
3 
4 
5 
6  7 
8 
9 
10 
SO_{p} conc. in ppm 
01.5 
1.53.0 
34.5 
4.56.0 
6.07.5 
7.59.0  9.010.5 
10.512 
1213.5 
13.515 
No. of observations 
l2 
l8 
6 
2 
4 
3  1 
1 
2 
1 
OR
Q2) a) Write a short note on methods of sampling. [4]
b) The following table gives the BOD in mg/l observed at a sampling station. Determine the Karl Pearson’s coefficient of skewness and coefficient of Kurtosis. [12]
Sr.No 
1 
2 
3  4  5  6 
7 
BOD (mg/l) 
010 
1020 
2030  3040  4050 
5060 
6070 
No. of observations 
8 
12 
20 
10 
6 
3 
1 
Q3) a) In the first week of August every year, the probability for a rainy day is 0.75. What is the probability that there will be exactly 5 rainy days in that week? What is the probability that there will be atmost 2 rainy days? [4]
b) The diameter D of wires installed in an Electro Static Precipitator (ESP) has a standard deviation of 0.01 in. What should be the value of mean if the probability of its exceeding 0.21 in is to be 1%. Use the std. normal table given in Q.4b. [4]
c)

Mechanical engineers while testing a new arc welding technique, classified welds with respect to appearance and Xray inspection. The results are shown in table below. Use the 0.05 level of significance to test the independence of the criteria of classification. [Use chisquare Table]. [8]
T <D O § <D d d < 
Bad 
Normal  Good 
Xray Inspection i 

Bad 
20 
7  3 
Normal 
13 
51  16 
Good 
7 
12  21 
OR
Q4) a) The ppm concentration of a toxic substance in a wastewater is known to be normally distributed with mean ^ = 100 and standard deviation a = 2.0. Calculate the probability that the toxic substance concentration C is [6]
i) less than 98
ii) between 98 and 104
iii) greater than 104
Use the standard normal distribution table given in Q.4b.
b) The following table gives tensile strength of concrete cylinders in lb/in^{2}. Test the goodness of fit for normal distribution at 5% significance level using chisquare test. [10]
Tensile strength of concrete cylinders 
No. of observations 
< 325 
6 
325 – 335 
6 
335 – 345 
11 
345 – 355 
14 
355 – 365 
16 
365 – 375 
15 
375 – 385 
8 
385 – 395 
10 
395 – 405 
8 
> 405 
6 
Use the following chisquare distribution table for a = 0.05.
u 
3  4  5  6 
7 
^^{2} 
7.8147  9.4877  11.07 
12.59 
14.067 
Use the Standard Normal Distribution Table given below.

z 
1.1 
1.2 
1.3 
1.4 
1.5 
1.6 
1.7 
1.8 
1.9 
2.0 
area 
0.3643 
0.3849 
0.4032 
0.4192 
0.4332 
0.4452 
0.4554 
0.4641 
0.4713 
0.4772 
z 
2.1 
2.2 
2.3 
2.4 
2.5 
area 
0.4821 
0.4861 
0.4893 
0.4918 
0.4938 
Q5) a) The pressure and volume of a gas are related by the equation
pv = a or 
Fit this equation 
v^{b} =^{1} a where a and b are constants ^{p}
[12] 
for the following data using the principle of least squares.
P 
0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
v 
1.62 
1.00 
0.75 
0.62 
0.52 
0.46 
b) For the following data find fg) using Newton’s forward interpolation formula. [6]
8 
10  12  14 
16 

A*) 
1000 
1900 
3250 
5400 
8950 
OR
Q6) a) The amount A of a substance remaining in a reacting system after an interval of time t in a certain chemical experiment is given in the following table. Find the value of A when t = 6. Use Lagrange’s Interpolation formula. [6]
t 
3 
7  9 
10 
A 
168 
120 
72 
63 
b) The average yearly rainfall over a basin and the corresponding yearly runoff, both expressed in cm, for a period of 9 years are given below. Establish the relation between rainfall and runoff of the form Y = ax + b. Also compute the coefficient of correlation between them. [12]
Year 
1 
2 
3 
4 
5 
6 
7 
8 
9 
Rainfall 
113 
127 
108 
167 
99 
152 
165 
160 
149 
Runoff 
74 
96 
59 
109 
57 
109 
124 
134 
106 
SECTION – II
Q 7) a) Solve the following system of equations by Gauss – elimination method. [8]
x_{x} + x_{2} + 2x_{Q} = 4 2x_{1} + 5x_{2} – 2x_{Q} = 3 x_{1} + 7x_{2} – 7x_{Q} = 5
b) Use Gauss – Seidel iterative method to solve the following equations. [The percent relative error E_{s} < 5%] [8]
83xj + 11x_{2} – 4x_{Q} = 95
7x_{x} + 52x_{2} + 13x_{Q} = 104
3x_{x} + 8x_{2} + 29x_{Q} = 71
OR
Q8) a) Solve the following equations using Gauss – Jordan method. [8]
2x_{x} + x_{2} + x_{Q} = 10 3x_{x} + 2x_{2} + 3x_{Q} = 18 xj + 4x_{2} + 9x_{Q} = 16
b) Use Gauss – Seidel iterative method to solve the following equations. [Relative error E < 5%] [8]
5* + x_{2} + 2x_{Q} = 19 x_{1} + 4x_{2} – 2x_{Q} = 2 2x_{1} + 3x_{2} + 8x_{Q} = 39
Q9) a) Find the positive real root of [8]
x log_{10} x = 1.2
Using bisection method in four iteration in the interval (2, 3)
b) Find the real root of x^{Q} – 3x + 1 = 0 lying between 1.5 and 2 upto three decimal places by Newton Raphson method. [8]
OR
QIO) a) Using False Position method, find the root of [10]
fx) = x^{2} – log_{e} x – 12 = 0
upto four iteration, in the interval (3, 4)
b) Explain – Newton Raphson method, to find the roots of the nonlinear equation. [6]
QII) a) A river is 80 m wide. The depthy in meter at a distance x from one bank is given by the following table. Calculate area of cross section of the river using Simpsons’s rule [9]
x 
0 
10 
20 
30 
40 
50 
60 
70 
80 
y 
0 
4 
7 
9 
12 
15 
14 
8 
3 
t _ 1 dx
b) Evaluate ^{1} = J 7 using Gauss Quadrature three point formula. [9]
0 1 + x
OR
QI2) a) The following table gives the velocity (v) of a particle at time (t) Find the distance moved by the particle in 12 seconds. [9]
t(sec) 
0 
2 
4 
6 
8 
10 
12 
v (m/s) 
4 
6 
16 
34 
60 
94 
136 
1 dx
b) Using Simpson’s 3/8^{th} rule. evaluate I = J . [9]