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Posted By: murali Member Level: Silver Posted Date: 28 Apr 2008
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2007 Jawaharlal Nehru Technological University B.Tech Mechanical Engineering PROBABILITY AND STATISTICS SET NO 4 Question paper
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Code No: R05220101 Set No. 4
II B.Tech II Semester Regular Examinations, Apr/May 2007
PROBABILITY AND STATISTICS
( Common to Civil Engineering, Mechanical Engineering, Chemical
Engineering, Mechatronics, Production Engineering, Bio-Technology and
Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) The probabilities that students A,B,C,D solve a problem are 1/3, 2/5, 1/5
and 1/4 respectively. If all of them try to solve the problem, what is the
probability that the problem is solved.
(b) In a bolt factory machines A,B,C manufacture 20%, 30% and 50% of the total
of their output and 6%, 3% and 2% are defective. A bolt is drawn at random
and found to be defective. Find the probabilities that it is manufactured from
i. Machine A
ii. Machine B
iii. Machine C [8+8]
2. (a) If X is a continuous random variable with distribution.
f(x) = 1
6x + k if 0 x 3
0 elsewhere
determine
i. the value of k
ii. the mean
iii. P(1 x 2)
(b) Derive the formula to find the mean and variance of Binomial distribution
[8+8]
3. (a) The probabilities of a poisson variate taking the values 1 and 2 are equal. Find
i. ยต
ii. p (x 1)
iii. p (1 < x < 4)
(b) In a sample of 1000 cases, the mean of a certain test is 14 and standard
deviation is 2.5. Assuming the distribution to be normal, find
i. how many students score between 12 and 15?
ii. how many score above 18
iii. how many score below 8 [8+8]
4. A population consists of five numbers 2,3,6,8,11. Consider all possible samples of
size two which can be drown without replacement from the population. Find
1 of 2
Code No: R05220101 Set No. 4
(a) The mean of the population
(b) Standard deviation of the population.
(c) The mean of the sampling distribution of means
(d) The standard deviation of the sampling distribution of means. [4+4+4+4]
5. (a) In a random sample of 125 cola drinkers, 68 said they prefer thums up to
pepsi. Test the null hypothesis p = .5 against the alternate hypothesis p>.5
(b) 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 478.6 to 495.4 [8+8]
6. Suppose during 400 five- minute intervals the ari-traffic control of an airport re-
ceived 0, 1,.........,12 messages and observed frequencies are given in the following
table.
No.of Messages
x 0 1 2 3 4 5 6 7 8 9 10 11 12
f 4 15 47 76 68 74 46 39 15 9 5 2 0
Test whether the Poisson distribution with ? = 4.5 provides a good fit to the above
data? [16]
7. (a) Fit a curve of the form y = aebx for the following data
x 0.0 .5 1.0 1.5 2.0 2.5
y .1 .45 2.15 9.15 40.35 180.75
(b) Find the most plausible values of x and y from the following equations x + 2y
= 6, 2x - y = 2, 2x - 5y = 7, 3x - 4y = - 4 [8+8]
8. (a) Find the coefficient of correlation between x and y for the following data
X 10 12 18 24 23 27
Y 13 18 12 25 30 10
(b) Show r =
2
x+y
-2
x
- 2
y
2x y
Where r = coefficient of correlation between x and y
s2
x, s2
y, s2
x+yare the variances of x, y and x+y respectively.
[8+8]
? ? ? ? ?
2 of 2
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