Jawaharlal Nehru Technological University Kakinada 2007 B.Tech Computer Science and Engineering PROBABILITY AND STATISTICS (1) - Question Paper

Code No: R059210501 Set No. 4
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) If A and B are any 2 arbitrary events of the sample space then Prove that
P( A U B) = P(A) + P(B) - P(A \ B)
(b) A issue in statistics is provided to 3 students A,B,C whose chances of solv-
ing it are 1
2 , 3
4 and 1
4 respectively. What is the probability that the issue
is solved.
(c) obtain the probability of getting a sum of 10 if we throw 2 dice. [5+5+6]
2. (a) For the continuous probability function f (x) = kx2 e-x when x _ 0 obtain
i. k
ii. mean
iii. variance
(b) 20% of items produced from a factory are defective. obtain the probability that
in a sample of five chosen at random.
i. none is defective
ii. 1 is defective
iii. p(1 < x < 4) [8+8]
3. (a) The avg. number of phone calls/minute coming into a switch board be-
tween two p.m. and 4. p.m. is 2.5. Determine the probability that during one
particular minute there will be
i. four or fewer
ii. more than six calls
(b) The marks found in mathematics by 1000 students is normally distributed
with mean 78% and standard deviation 11%. Determine
i. how many students got marks above 90%
ii. what was the highest mark found by the least 10% of the learner
iii. within what limits did the middle of 90% of the students lie [8+8]
4. Samples of size two are taken from the population 4, 8, 12, 16, 20, 24 without re-
placement. obtain
(a) mean of the population
(b) standard deviation of population
(c) the mean of sampling distribution of means
1 of 2
(d) standard deviation of sampling distribution of means. [16]
5. (a) In a study of an automobile insurance a random sample of 80 body repair
costs had a mean of Rs. 472.35 and a standard deviation of Rs 62.35. If x is
used as a point estimate to the actual avg. repair costs, with what confidence
we can assert that the maximum fault doesn’t exceed Rs. 10. obtain also the
confidence interval with that confidence.
(b) A manufacturer of electric bulbs claims that the percentage defectives in his
product doesn’t exceed 6. A sample of 40 bulbs is obtained to contain five defectives.
Would you consider the claim justified? [8+8]
6. (a) It has been suggested that an avg. college teacher in Andhra Pradesh
spends less than 10 hours in a week on his own academic schedule. The
figures for the time spent during a week are provided beneath for 12 teachers.
7.1 13.1 7.8 3.6 8.4 4.9
9.6 3.4 0.1 7.2 20.3 11.1
Is the claim justified with the level of significance of 0.05?
(b) Test of the fidelity and the selectivity of 190 radio receivers produced the
outcomes shown in the subsequent table: [8+8]
Fidility
Low avg. High
Low six 12 32
Selectivity avg. 33 61 18
High 13 15 0
7. Fit an formula of the form Y=abx to the subsequent data: [16]
x: two three four five 6
y: 144 172.8 207.4 248.8 298.5
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.