JNTU Kakinada B-Tech 1-2 R1621011 PROBABILITY AND STATISTICS (Civil Engineering) R16 May 2018 Question Paper

Code No: R1621011
II B. Tech I Semester Supplementary Examinations, May – 2018
PROBABILITY AND STATISTICS (Civil Engineering)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Define a discrete random variable and give an example. (2M)
b)Define a distribution function for a continuous random variable. (2M)
c) Find the value of the finite population correction factor for 10 n= and
1000 N = . (2M)
d)Define null and alternative hypothesis. (3M)
e)Define simple correlation and write formula for simple correlation coefficient. (3M)
f)Write the expression for the control line and three sigma for mean Chart (2M)
PART -B
2. a) An experiment consists of four tosses of a coin. Denoting the outcomes HHTH,
THTT, ?.and assuming that all 16 outcomes are equally likely, find the
probability distribution for the total number of heads. (7M)
b) Define the geometric distribution and find its mean and variance. (7M)
3. a) Let X be a continuous random variable with distribution :

2
0 1( )
0
k x if x
f x
elsewhere
? = =
=
?
?(i) Evaluate k (ii) Find (1 / 4 3 / 4). p X = = (iii) Find ( 2 / 3). p X > (7M)
b) Define the Gamma Distribution and find its mean and variance. (7M)
4. a) Take 30 slips of paper and label five each with 4 – and 4,four each with 3 – and
3,three each with 2 – and 2, and two each with 1 – ,0 and 1.If each slip of paper has
the same probability of being drawn , find the probability of getting
4, 3, 2, 1, 0, 1, 2, 3, 4 – – – – and find the mean and the variance of this
distribution. (7M)
b)Find the value of
0.95
F for
1 2
12 15 and ? ? = = degrees of freedom. (7M)
5. a) A trucking firm is suspicious of the claim that the average lifetime of certain tires
is at least 28,000 miles. To check the claim, the firm puts 40 of these tires on its
trucks and gets a mean life time of 27, 463 miles with a standard deviation of 1,
348 miles. What can it conclude if the probability of a Type I error is to be at most
0.01? (7M)
b)Explain procedure for one-way classification of analysis of variance. (7M)
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SET – 1
R16

Code No: R1621011
II B. Tech I Semester Supplementary Examinations, May – 2018
PROBABILITY AND STATISTICS (Civil Engineering)Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B) 2. Answer ALL the question in Part-A
3. Answer any FOUR Questions from Part-B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
PART ?A
1. a)Define a discrete random variable and give an example. (2M)
b)Define a distribution function for a continuous random variable. (2M)
c) Find the value of the finite population correction factor for 10 n= and
1000 N = . (2M)
d)Define null and alternative hypothesis. (3M)
e)Define simple correlation and write formula for simple correlation coefficient. (3M)
f)Write the expression for the control line and three sigma for mean Chart (2M)
PART -B
2. a) An experiment consists of four tosses of a coin. Denoting the outcomes HHTH,
THTT, ?.and assuming that all 16 outcomes are equally likely, find the
probability distribution for the total number of heads. (7M)
b) Define the geometric distribution and find its mean and variance. (7M)
3. a) Let X be a continuous random variable with distribution :

2
0 1( )
0
k x if x
f x
elsewhere
? = =
=
?
?(i) Evaluate k (ii) Find (1 / 4 3 / 4). p X = = (iii) Find ( 2 / 3). p X > (7M)
b) Define the Gamma Distribution and find its mean and variance. (7M)
4. a) Take 30 slips of paper and label five each with 4 – and 4,four each with 3 – and
3,three each with 2 – and 2, and two each with 1 – ,0 and 1.If each slip of paper has
the same probability of being drawn , find the probability of getting
4, 3, 2, 1, 0, 1, 2, 3, 4 – – – – and find the mean and the variance of this
distribution. (7M)
b)Find the value of
0.95
F for
1 2
12 15 and ? ? = = degrees of freedom. (7M)
5. a) A trucking firm is suspicious of the claim that the average lifetime of certain tires
is at least 28,000 miles. To check the claim, the firm puts 40 of these tires on its
trucks and gets a mean life time of 27, 463 miles with a standard deviation of 1,
348 miles. What can it conclude if the probability of a Type I error is to be at most
0.01? (7M)
b)Explain procedure for one-way classification of analysis of variance. (7M)
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Code No: R1621011
6. a) The following are the measurements of the air velocity and evaporation coefficient
of burning fuel droplets in an impulse engine:
Air
velocity(cm/s)x
20 60 100 140 180 220 260 300 340 380
Evaporation
coefficient (mm
2
/s) y
0.18 0.37 0.35 0.78 .056 .075 1.18 1.36 1.17 1.65
Fit a straight line to these data by the method of least squares and use it to estimate
the evaporation coefficient of a droplet when the air velocity is 190 cm/s. (7M)
b) Find the Correlation Coefficient for the following data:
x 1 2 3 4 5
y 2 5 3 8 7 (7M)
7. Consider the following data taken on subgroups of size 5. The data contain 20
averages and ranges on the diameter (in millimeters) of an important component
part of an engine. Display X
and R Charts. Does the process appear to be in
control?
Sample
X R Sample
X R
1 2.3972 0.0052 11 2.3887 0.0082
2 2.4191 0.0117 12 2.4107 0.0032
3 2.4215 0.0062 13 2.4009 0.0077
4 2.3917 0.0089 14 2.3992 0.0107
5 2.4151 0.0095 15 2.3889 0.0025
6 2.4027 0.0101 16 2.4107 0.0138
7 2.3921 0.0091 17 2.4109 0.0037
8 2.4171 0.0059 18 2.3944 0.0052
9 2.3951 0.0068 19 2.3951 0.0038
10 2.4215 0.0048 20 2.4015 0.0017 (14M)

Note :- Statistical tables and Control Chart Constants are required

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