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Posted By: sunil Member Level: Diamond Posted Date: 26 Jun 2008
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2007 Jawaharlal Nehru Technological University Chemical engineering II B.Tech II Semester Regular Examinations, Aug/Sep 2007 PROBABILITY AND STATISTICS Question paper
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Code No: R05220101
Set No. 1
II B.Tech II Semester Supplimentary Examinations, Aug/Sep 2007
PROBABILITY AND STATISTICS
( Common to Civil Engineering, Mechanical Engineering, Chemical
Engineering, Mechatronics, Production Engineering, Bio-Technology and
Automobile Engineering)
Time: 3 hours
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
Max Marks: 80
1. (a) If P(A) = 1/2, P(B) = 1/3, P(A nB) = 1/5, then ?nd
i. P(AUB)
ii. P(Acn B )
iii. P(A n Bc)
iv. P(Acn Bc)
where (Ac= the compliment of A)
(b) Three machines produces 70%, 20% and 10% of the total number of a fac-
tory.The percentage of defective output of these machines are 4%, 3% and 2%
respectively. An item is selected at random and found defective. Find the
probability that it is from
i. machine-I
ii. machine-II
iii. machine-III
2. (a) Suppose a continuous random variable X has the probability density
f(x)=k(1 - x2) for 0 < x < 1, and f(x) = 0 otherwise. Find
i. k
ii. mean
iii. variance.
[8+8]
(b) The probability that john hits a target is12 He ?res 6 times. Find the proba-
bility that he hits the target
i. exactly 2 times
ii. more than 4 times
iii. at least once.
[8+8]
3. (a) A Poisson distribution has a double mode at x = 2 and x = 3, ?nd the
maximum probability and also ?nd p(x=2).
(b) The weekly wages of 1000 workers are normally distributed around a mean of
Rs.70 and S.D of Rs.5/- Estimate the number of workers whose weekly wages
will be
i. between Rs.70 and Rs.72
ii. between 69 and 72.
1 of 3
[8+8]
Code No: R05220101
Set No. 1
4. Samples of size 2 are taken from the population 4, 8, 12, 16, 20, 24 without re-
placement. Find
(a) mean of the population
(b) standard deviation of population
(c) the mean of sampling distribution of means
(d) standard deviation of sampling distribution of means.
[16]
5. (a) A random sample of size 81 was taken whose varience is 20.25 and mean 32
construct 98% con?dence interval
(b) A manufacturer claims that only 4% of his products are defective. A random
sample of 500 were taken among which 100 defective Test the hypothesis at
.05 level.
[8+8]
6. (a) To examine the hypothesis that the husbands are more intelligent than the
wives, an investigator took a sample of 10 couples and administered them a
test which measures the IQ as follows:
Test the hypothesis with a reasonable test at the level of signi?cance of 0.05?
Husbands: 117 105 97 105 123 109 86 78 103 107
Wives
106 98 87 104 116 95 90 69 108 85
(b) In an investigation on the machine performance the following results were
obtained:
No.of Units inspected No. of defectives
Machine 1
Machine 2
375
450
17
22
Test whether there is any signi?cant performance of two machines at a=0.05
[8+8]
7. (a) The measurements of humidity and the moisture content in a raw material
are given in the following table. Fit a St. line of the for y = ax + b Humidity
(x)
42 35 50 43 48 62 31 36 44 39 55 48
12 8 14 9 1 16 7 9 12 10 13 11
(b) Find the most plausible values of x and y
x + 2y - 7 = 0 2x + 3y - -2 = 0
x + 8y - 3 =0 3x - y + 5 = 0.
[8+8]
8. (a) A sample of 12 fathers and their eldest sons gave the following data about
their height in inches calculate the coe?cient of rank correlation.
Fathers 65 63 67 64 68 62 70 66 68 67 69 71
Sons 68 66 68 65 69 66 68 65 71 67 68 70
[8+8]
(b) Given that x = 4y + 5 and y = k x +4 are the regression lines of x on y and y
on x, respectively, show that 0 = k = 25. If k = 0.10 actually, ?nd the means
of the variables x and y and also their coe?cient of correlation.
2 of 3
Code No: R05220101
? ? ? ? ?
3 of 3
Set No. 1
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