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Posted By: CONFIDENCE IS THE COMPANION OF SUCCESS Member Level: Diamond Posted Date: 16 Apr 2008
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2007 Anna University B.Tech Computer Science & Engineering Probability And Statistics Question paper
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B.Tech I Semester Regular Examinations, November 2007
PROBABILITY AND STATISTICS
( Common to Computer Science & Engineering, Information Technology
and Computer Science & Systems Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) If A and B are any two arbitrary events of the sample space then Prove that
P( A U B) = P(A) + P(B) - P(A \ B)
(b) A problem in statistics is given to three students A,B,C whose chances of solving it are 1
2 , 3
4 and 1
4 respectively. What is the probability that the problem
is solved.
(c) Find the probability of getting a sum of 10 if we throw two dice. [5+5+6]
2. (a) For the continuous probability function f (x) = kx2 e-x when x 0 find
i. k
ii. mean
iii. variance
(b) 20% of items produced from a factory are defective. Find the probability that
in a sample of 5 chosen at random.
i. none is defective
ii. one is defective
iii. p(1 < x < 4) [8+8]
3. (a) The average number of phone calls/minute coming into a switch board be-
tween 2 p.m. and 4. p.m. is 2.5. Determine the probability that during one
particular minute there will be
i. 4 or fewer
ii. more than 6 calls
(b) The marks obtained 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 obtained by the lowest 10% of the student
iii. within what limits did the middle of 90% of the students lie [8+8]
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
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 true average repair costs, with what confidence
we can assert that the maximum error doesn’t exceed Rs. 10. Find 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 found to contain 5 defectives.
Would you consider the claim justified? [8+8]
6. (a) It has been suggested that an average 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 given below 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
results shown in the following table: [8+8]
Fidelity
Low Average High
Low 6 12 32
Selectivity Average 33 61 18
High 13 15 0
7. Fit an equation of the form Y=abx to the following data: [16]
x: 2 3 4 5 6
y: 144 172.8 207.4 248.8 298.5
8. A chemical company wishing to study the elect of extraction time on the efficiently
of an extraction operation obtained in the data shown in the following table.
Extraction time x 27 45 41 19 35 39 19 49 15 31
Extraction efficiency + 57 64 80 46 62 72 52 77 57 68
Calculate the coefficient of correlation between x and y and the two lines of re [gression16]
? ? ? ? ?
2 of 2
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