Jawaharlal Nehru Technological University Kakinada 2007 B.Tech Computer Science and Engineering PROBABILITY AND STATISTICS (2) - Question Paper

Code No: R059210501 Set No. 3
II B.Tech I Semester Regular Examinations, November 2007
PROBABILITY AND STATISTICS
( Common to Computer Science & Engineering, info Technology
and Computer Science & Systems Engineering)
Time: three hours Max Marks: 80
ans any 5 ques.
All ques. carry equal marks
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1. (a) Of the 3 men, the chances that a politician, a businessman or an acad-
emician will be appointed as a Vice-Chancellor (V.C.) of a University are 0.5,
0.3, 0.2 respectively. Probability that research is promoted by these persons
if they are appointed as V.C. are 0.3, 0.7, 0.8 respectively.
i. Determine the probability that research is promoted
ii. If research is promoted, what is the probability that V.C. is an academi-
cian
(b) There are 2 boxes inbox I, 11 cards are there numbered one to 11 and in
box II, five cards numbered one to 5. A box is chosen and a card is drawn. If the
card indicates an even number then a different card is drawn from the identical box. If
card indicates an odd number a different card is drawn from the other box. obtain
the probability that
i. both are even
ii. both are odd
iii. if both are even. What is the probability that they are from box I. [8+8]
2. (a) describe random variable, discrete probability distribution, continuous proba-
bility distribution and cumulative distribution. provide an example of every.
(b) The mean of Binomial distribution is three and the variance is 9
4 . obtain
i. The value of n
ii. p(x _ 7)
iii. p(1 _ x < 6). [8+8]
3. (a) avg. number of accidents on any day on a national highway is 1.8. Deter-
mine the probability that the number of accidents are
i. at lowest one
ii. at most one
(b) If X is a normal variate, obtain the probability
i. to the left of z = –1.78
ii. to the right of z = – 1.45
iii. corresponding to – 0.80 _ z _ 1.53
iv. to the left of z= – 2.52 and to the right of z= 1.83. [8+8]
1 of 2
4. (a) A random sample of size 81 is taken from an infinite population having the
mean 65 and standard deviation 10. What is the probability that x will be
ranging from 66 and 68?
(b) Write about
i. Critical region
ii. 2 tailed test. [8+8]
5. (a) A random sample of size 100 has a standard deviation of 5. What can you say
about the maximum fault with 95% confidence.
(b) Among 900 people in a state 90 are obtained to be chapatti eaters. Construct
99% confidence interval for the actual proportion.
(c) A random sample of 1200 apples was taken from a large consignment and
obtained that 10% of them are bad. The supplier claims that only 2% are bad.
Test his claim at 95% level. [5+5+6]
6. Measurements of the fat content of 2 types of ice creams brand A and brand B
yielded the subsequent sample data.
Brand A 13.5 14.0 13.6 12.9 13.0
Brand B 12.9 13.0 12.4 13.5 12.7
Test the significant ranging from the means at 0.05 level. [16]
7. (a) Derive normal equations to fit the parabola y = a0 + a1x + a2x
2
(b) Fit the parabola y = a0 + a1x + a2x
2 for the subsequent data [6+10]
X 0 one two three 4
Y one 1.8 1.3 2.5 6.3
8. A chemical company wishing to study the effect of extraction time on the efficiently
of an extraction operation found in the data shown in the subsequent table.
Extraction time x 27 45 41 19 35 39 19 49 15 31
Extraction efficiency y 57 64 80 46 62 72 52 77 57 68
compute the coefficient of correlation ranging from x and y and the 2 lines of regres-
sion. [16]
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Earning:   Approval pending.