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Posted By: srinivas Member Level: Gold Posted Date: 28 May 2008
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2008 Andhra Pradesh State Jawaharlal Nehru Technological University B.Tech PROBABILITY AND STATISTICS Question paper
Code No: RR220105 Set No. 3
II B.Tech II Semester Supplimentary Examinations, Apr/May 2008
PROBABILITY AND STATISTICS
( Common to Civil Engineering, Mechanical Engineering, Computer Science
& Engineering, Chemical Engineering, Information Technology,
Mechatronics, Computer Science & Systems Engineering, Electronics &
Computer Engineering, Production Engineering, Bio-Technology and
Automobile Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Out of 15 items 4 are not in good condition. 4 are selected at random. Find
the probability that
i. All are not good
ii. Two are not good
(b) If A and B are any two events, then prove that P(AUB) = P(A) + P(B) -
P(A \ B).
(c) In a class 2% of boys and 3% of girls are having blue eyes. There are 30%
girls in the class. If a student is selected and having blue eyes, what is the
probability that the student is girl. [8+8]
2. (a) Find the variance of the binomial distribution .
(b) Determine the probability distribution of the number of bad eggs in a basket
containing 6 eggs given that 10% of eggs are bad in a large consignment[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. (a) Suppose that we want to investigate whether on the average men earn more
than Rs.20 per week more then women in a certain industry. A sample data
show that 60 men earn on the average while 60 women earn on an average
x2 = 266.10 per week with a standard deviation of Rs.18.20, what can we
conclude at 0.01 level of significance?
1 of 2
Code No: RR220105 Set No. 3
(b) A sample of 900 members has a mean 3-4cms and S.D 2.61cms. Is this sample
has been taken from a large population of mean 3.25cms and S.D 2.61cms.
[8+8]
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) Five measurements of tar content of a certain kind of cigarettes yielded 14.5,
14.2, 14.4, 14.3 and 14.6 mg per cigarettes. Show that the difference between
the mean of this sample
-x
= 14.4, and the average tar claimed by the manu-
facturer ยต = 14.0, is significant at a = 0.05. Assume normality?
(b) Mechanical Engineers, testing a new arc welding technique, classified welds
both with respect to appearance and an X-ray inspection.
Quality
Bad Normal Good Total
Bad 20 7 3 30
X-ray Normal 13 51 16 80
Good 7 12 21 40
Total 40 70 40 150
Test for independence using a = 0.05 and find the individual cell contribution
to the ?2 - statistic. [8+8]
7. (a) Fit a straight line y = a + bx for the following data
x 1 2 3 4 5 6
y 14 33 40 63 76 85
(b) Fit a curve of the y = axb for the following data [8+8]
x 1 2 3 4 5
y .5 .2 4.5 8 12.5
8. Use the formula ? =
2
x+y
-2
x
- 2
y
2
x
y
to compute the correlation coefficient to the
following data
x : 62 56 36 66 25 75 82 78
y : 58 44 51 58 60 68 62 84 [16]
? ? ? ? ?
2 of 2
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