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Posted By: satish Member Level: Gold Posted Date: 12 Feb 2008
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2006 Jawaharlal Nehru Technological University B.E Computer Science PROBABILITY AND STATISTICS II B.Tech I Semester Supplementary Examinations, Apr/May 2006 Question paper
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Code No: NR220105 NR
II B.Tech I Semester Supplementary Examinations, Apr/May 2006
PROBABILITY AND STATISTICS
(Common to Civil Engineering, Computer Science & Engineering,
Chemical Engineering, Information Technology, Computer Science &
Systems Engineering, Electronics & Computer Engineering and Production
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) If the probability that a communication system will have high fidelity
is 0.81 and the probability that it will have high fidelity and high
selectivity is 0.18. What is probability that a system will high fidelity
will also have high selectivity.
(b) If the probability that a research project will be well planned is 0.80
and the probability that it will be planned and well executed is 0.72.
What is the probability that a research project that is well planned will
also be well executive.
[8+8]
2. (a) The mean and variance of a binomial distribution are 4 and 4/3
respectively.Find P(X _ 1).
(b) The mark of 1000 students in a University are found to be normally
distributed with mean 70 and S.D 5. Estimate the number of students
whose marks will be
i. between 60 and 75
ii. more than 75
iii. less than 68.
[6+10]
3. (a) From a lot of 10 items containing 3 defective , a sample of 4 items is
drawn at random. Let the random variable X denote the number of
defective items in the sample. If the sample is drawn without
replecement
i. Find the probability distribution of X
ii. Find P(X _ 1) and P(0 < X < 2).
(b) Define nornal distribution. Find its mean and variance.
1 of 1 [8+8]
4. (a) 500 articles were selected at random out a batch containing 10000
articles and 30 were found to be defective. How many defective articles
would you reasonably expect to have in the whole batch?
(b) Out of consignment of 100000 tennis balls 496 were selected at
random and examined and it was found that 20 of these were
defective. How many defective balls can you reasonably expect to
have in the whole consignment at 95% confidence level?
[8+8]
5. (a) In a sample of 600 men from a certain large city 450 are found to be
smokers.‘In one of 900 from another city 450 are smokers. Do the data
indicate that the cities are significantly different with respect ’to
prevalence of smoking among men?
(b) Random samples of 400 men and 600 women in a locality were asked
whether they would like to have a bus stop ’near their residence. 200
men and 325 women were in favour of the proposal. Test the
hypothesis that proportions of men and women in favour of the
proposals are same in the male and female. Discuss at 5% level of
significance.
[8+8]
6. (a) It is desired to test the hypothesis µ0 = 40 against the alternative
hypothesis µ1 = 42 on the basis of a random sample from a normal
population with the standard deviation _ = 4. If the probability of a
Type 1 error is to be 0.05 and the probability of a Type II error is to be
0.24, find the required size of the sample.
(b) The diameter of rotor shafts in a lot has a mean of 0.249 inch and a
standard deviation of 0.003 inch. The inner diameters of bearings in
another lot have a mean of 0.255 inch and a standard deviation of
0.002 inch.
(i) What are the mean and the standard deviation of the clearances
between shafts and bearings selected from these lots?
(ii) If a shaft and a bearing are selected at random, what is the
probability that the shaft will not fit inside the bearing?
(Assume that both dimensions are normally distributed).
[8+8]
4. (a) 500 articles were selected at random out a batch containing 10000
articles and 30 were found to be defective. How many defective articles
would you reasonably expect to have in the whole batch?
(b) Out of consignment of 100000 tennis balls 496 were selected at
random and examined and it was found that 20 of these were
defective. How many defective balls can you reasonably expect to
have in the whole consignment at 95% confidence level?
[8+8]
5. (a) In a sample of 600 men from a certain large city 450 are found to be
smokers.‘In one of 900 from another city 450 are smokers. Do the data
indicate that the cities are significantly different with respect ’to
prevalence of smoking among men?
(b) Random samples of 400 men and 600 women in a locality were asked
whether they would like to have a bus stop ’near their residence. 200
men and 325 women were in favour of the proposal. Test the
hypothesis that proportions of men and women in favour of the
proposals are same in the male and female. Discuss at 5% level of
significance.
[8+8]
6. (a) It is desired to test the hypothesis µ0 = 40 against the alternative
hypothesis µ1 = 42 on the basis of a random sample from a normal
population with the standard deviation _ = 4. If the probability of a
Type 1 error is to be 0.05 and the probability of a Type II error is to be
0.24, find the required size of the sample.
(b) The diameter of rotor shafts in a lot has a mean of 0.249 inch and a
standard deviation of 0.003 inch. The inner diameters of bearings in
another lot have a mean of 0.255 inch and a standard deviation of
0.002 inch.
(i) What are the mean and the standard deviation of the clearances
between shafts and bearings selected from these lots?
(ii) If a shaft and a bearing are selected at random, what is the
probability that the shaft will not fit inside the bearing?
(Assume that both dimensions are normally distributed).
[8+8]
7. Estimate r by fitting the ideal gas law PV r = c to the following data.
=------------------------------------------------------------------------
Pressure(lb/in 2 ) 16.6 39.7 78.5 115.5 195.3 546.1
---------------------------------------------------------------------------
VolumeV (IN 3 ) 50 30 20 15 10 5
------------------------------------------------------------------------
[8+8]
8. Fit a regression plane to estimate _o, _1 , _2 to the following data of a
transport
company on the weights of 6 shipments, the distances they were moved and
the
damage of the goods that was incurred. Estimate the damage when a
shipment of
3700kg is need to a distance of 260 km.
-----------------------------------------------------------------------
Weight x1(1000kg) 4.0 3.0 1.6 1.2 3.4 4.8
------------------------------------------------------------------------
Distance x2(100km) 1.5 2.2 1.0 2.0 0.8 1.6
-----------------------------------------------------------------------
Damage y(Rs) 160 112 69 90 123 186
[16]
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