Jawaharlal Nehru Technological University Kakinada 2007 B.Tech Computer Science and Engineering PROBABILITY AND STATISTICS (4) - Question Paper

Code No: R059210501 Set No. 1
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 events with P(A) = 1/3, P(B) = 1/4, and P(A U B) = 1/2,
find
i. P(A/B)
ii. P(A \Bc )
(b) 3 students A,B,C are in a running race. A and B have the identical probability
of wining and every is twice as likely to win as C. obtain the probability that B
or C wins.
(c) The students in a class are opted at random 1 after the other for an
examination. obtain the probability that the boys and girls are alternate if
there are
i. five boys and four girls
ii. four boys and four girls. [6+5+5]
2. (a) If X is a continuous random variable and K is a constant then prove that
i. Var (X+K) = Var (X)
ii. Var(kX) = k2 Var (X)
(b) Determine the probability of getting nine exactly twice in three throws with a pair
of fair dice. [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
1 of 2
(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 lady stenographer claims that she can take dictation at the rate of 118
words per minute can we reject her claim on the basis of 100 trials in which
she demonstrates a mean of 116 words and a S.D of 15 words.
(b) In a large consignment of oranges a random sample of 64 oranges revealed
that 14 oranges were bad. If it reasonable to ensure that 20% of the oranges
are bad? [8+8]
6. (a) The measurements of the output of 2 units have provided the subsequent outcomes.
Assuming that both samples have been level whether the 2 populations have
the identical varience.
Unit-A 14.1 10.1 14.7 13.7 14.0
Unit-B 14.0 14.5 13.7 12.7 14.1
(b) The subsequent are the samples of skills. Test the significant difference ranging from
the means at .05 level. [8+8]
Sample-I 74.1 77.7 74.4 74 73.8 -
Sample-II 70.8 74.9 74.2 70.4 69.2 72.2
7. (a) Fit the curve y = aebx to the subsequent data
x: 0 one two three four five six seven 8
y: 20 30 52 77 135 211 326 550 1052
(b) Fit a 2nd degree polynomial to the subsequent data, taking x as independent
variable: [8+8]
x: one two three four five six seven eight 9
y: two six seven eight 10 11 11 10 15
8. (a) A sample of 12 fathers and their eldest sons gave the subsequent data about
their height in inches compute the coefficient of rank correlation. [8+8]
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
(b) provided that x = 4y + five 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, obtain the means
of the variables x and y and also their coefficient of correlation.
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Earning:   Approval pending.