Hall Ticket No Question Paper Code: AHS010
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech III Semester End Examinations (Regular) November, 2018
Regulation: IARE R16
PROBABILITY AND STATISTICS
Time: 3 Hours (Common to ME CE) Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. A random variable X has the density function:
Cx if0 x 2
otherwise:
Determine C and find mean and variance of x.
The probability that the noise level of a wide-band amplifier will exceed 2 dB is 0.05. Find the
probabilities that among 12 such amplifiers the noise level of
One will exceed 2 dB
At most two will exceed 2 dB
Two or more will exceed 2 dB.
2. A random variable x has the following probability function as shown in Table
Table 1
X 0 1 2 3 4 5 6 7
0 k 2k 2k 3k k2 2 k2 7 k2+k
Compute E V
The time required to assemble a piece of machinery is a random variable having approximately
a normal distribution with 12.9 minutes and 2.0 minutes. What are the probabilities
that the assembly of a piece of machinery of this kind will take
at least 11.5 minutes
anywhere from 11.0 to 14.8 minutes.
UNIT II
3. The joint probability mass function of is given by P k (2x x 2 and
y 3. Find
The value of k
The marginal distributions.

Page 1 of 4
The ranking of 10 students in two subjects A and B are as shown in Table
Table 2
3 5 8 4 7 10 2 1 6 9
6 4 9 8 1 2 3 10 5 7
Calculate the rank correlation coefficient.

4. From the following joint distribution of X and Y as shown in Table 3
Table 3
X/Y 1 2 3 4 5 6
0 0 0 1/32 2/32 2/32 3/32
1 1/16 1/16 1/8 1/8 1/8 1/8
2 1/32 1/32 1/64 1/64 0 2/64
Find
P
X

The following scores shown in Table eight students obtained in the midterm 1 and 2 examinations
in a course in Probability and Statistics:
Table 4
Mid Term 1 Examinations 22 26 29 30 31 31 34 35
Mid Term 2 Examinations 20 20 21 29 27 24 27 31
Find the regression equations.

UNIT III
5. Construct sampling distribution of means for the population 11 by drawing sample of size
two with replacement. Determine population mean population variance the mean of
sampling distribution of means standard error.
A random sample of size 100 is taken from an infinite population having the mean 76 and
the variance is 256. What is the probability that
Y will be between 75 and 78?
6. If ordered samples of size n=2 are drawn with replacement from the population 8}.
Determine population mean population variance the mean of sampling distribution
of means standard error.
Page 2 of 4
A random sample of 100 teachers in a large metropolitan area revealed a mean weekly salary of
Rs. 487 with a standard deviation Rs.48. With what degree of confidence can we assert that the
average weekly salary of all teachers in the metropolitan area is between 472 to 502?
UNIT IV
7. Random samples of 400 men and 600 women were asked whether they would like to have a flyover
near their residence. 200 men and 325 women were in fovour of the proposal. Test the hypothesis
that proportions of men and women in fovour of the proposal are the same against that they are
not at level.
A random sample of size 500, the mean is found to be 20. In another independent sample of size
400, the mean is 15. Could the samples have been drawn from the same population with S.D.

8. The mean of two samples of 1000 and 2000 members are respectively 67.5 and 68 inches. Can
they be regarded as drawn from the same population with S.D. 2.5 inches?
In a certain city 380 men out of 800 are found to smokers. Discuss whether this information
supports the view that majority of men in this city are non-smoker?
UNIT V
9. A sample of 26 bulbs gives a mean life of 900 hours with S.D. of 20 hours. The manufactures
claims that the mean life of bulbs is 1000 hours. Is the sample not upto the standard?
The following data shown in Table 5 represent the number of units of production per day turned
out by four randomly chosen operators using three machines.
Table 5
Operators M1 M2 M3
1 150 151 156
2 147 159 155
3 141 146 153
4 154 152 159
Carry out analysis of variance and write your conclusion.
10. A trucking firm is suspicious of the claim that the average life time 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 27,462 miles with a S.D of 1,348 miles. What can it conclude if the probability of a
type-I error is to be at most 0.01?
Page 3 of 4
The internal bonding strength of 3 different resins ED, MD and PF need to be compared. Five
specimens were prepared with each of the resins.Test at the level of significance of 0.01 whether
the differences among the sample means can be attributed to chance.
Table 6
Resin Strength
ED 0.99 1.19 0.79 0.95 0.90
MD 1.11 1.53 1.37 1.24 1.42
PF 0.83 0.68 0.94 0.86 0.57