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Name
Reg No

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
07 THRISSUR CLUSTER
FIRST SEMESTER M.TECH. DEGREE EXAMINATION DEC 2017
Department of Civil Engineering
(common for EE and WR&HI)
07MA6001 APPLIED STATISTICS
Time 3 hours Max .Marks: 60
Answer all six questions. Part of each question is compulsory.
Answer either part or part of each question
Q.no.
Module 1
Marks
1a The height of students is normally distributed with mean 54 and SD 12 inches.
What percentage of students has height between 46 and 56 inches?
4
Answer b or c
b
Given the pdf of X as
0 5
− 5 10
Find the value of k and P
5
c The time in years to failure of certain components of a system is a random variable
following exponential distribution with mean β=5. If 5 of these components are in different
systems,find the probability that at least 2 components are still functioning at the end of 8
years.
5
Q.no.
Module 2
Marks
2a In a partially destroyed record of correlation data of X and Variance of X is 9 and the
regression equations are 8x-10y+66=0 and 40x-18y=214.Find the mean values of X and Y
and the correlation coefficient between them.
4
Answer b or c
b Calculate the correlation coefficient between X and Y from
X 98 70 40 20 85 75 95 80 10 5
Y 85 65 32 30 80 60 80 70 20 10
5
c Find r12.3 and R1.23 if r12=0.6 ,r13=0.7 0.65 5
Q.no. Module 3 Marks
3a Explain the sampling distributions of mean. 4
Answer b or c
b State central limit theorem. Use this to find the probability that the error will be less than
1.2 if the mean of a random sample of size 25 is used to estimate the mean of an infinite
population with SD 2.4.
5
c If independent random samples of sizes n1=n2=8 came from a normal population having
same variance, what is the probability that either sample variance will be at least 7 times
as large as the other.
5
Q.no.
Module 4
Marks
4a If x1,x2,....xn is a random sample from show that
1

Σ
2 is an unbiased estimator of 4
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Answer b or c
b Obtain the maximum likelihood estimates of α and β for a random sample from
is a constant.
5
c Given a random sample of size 9 from 8.6, 7.9, 8.3, 6.4, 8.4, 9.8, 7.2,
7.8, 7.6. Construct 90% confidence interval
5
Q.no. Module 5 Marks
5a
A machinist is making engine parts with axle diameters of 0.700 inch. A random sample of 10 parts
shows a mean diameter of 0.742 inches with a SD of 0.040 inch. Test whether the work meets the
specification.
5
Answer b or c
b In a year, there are 956 births in a town of which 52.5% are males, while in towns A and
B combined, this proportion in a total of 1406 births was 0.496.
Is there any significant difference in the proportion of male births in the two towns?
7
c Fit a Poisson distribution to the data and test the goodness of fit
x 0 1 2 3 4 5
f 142 156 69 27 5 1
7
Q.no. Module 6 Marks
6a
What are the components of a time series?
5
Answer b or c
b
Three different machines are used for a population on the basis of the outputs. Test whether the
machines are equally effective.
Outputs
Machines
10 9 20
15 7 16
11 5 10
10 6 14
7
c The following table gives the number of refrigerators sold by 4 salesman A and D in
3 months
Month
↓
A B C D
I 50 40 48 39
II 46 48 50 45
III 39 44 40 39
Is there any significant difference in the sale made by the four salesman
7
(Note: The sub question will be compulsory one, testing the knowledge on fundamental aspects. Parts and
shall preferably be application type questions with the choice to answer any one.)