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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 Computer Science & Engineering PROBABILITY AND STATISTICS Question paper
Code No: RR220105 Set No. 1
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) The probabilities of passing in subject A, B, C, D are 3/4, 2/3, 4/5 and 1/2
respectively. To qualify in the examination a student should pass in A and
two subjects among the three what is the probability of qualifying in that
examination.
(b) There are two boxes. In box -I, 11 cards are there numbered 1 to 11 and in
box-II, 5 cards numbered 1 to 5. A box is chosen and a card is drawn. If the
card shows an even number then another card is drawn from the same box. If
card shows an odd number another card is drawn from the other box. Find
the probability that
i. Both are even
ii. Both are odd
iii. If both are even, it is from box I. [8+8]
2. (a) For the continuous probability function f (x) = kx2 e-x 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) Find the probability that at most 5 defective components will be found in a
lot of 200 it experience. Shows that 2% of such components are defective.
Also find the probability of more than five defective components.
(b) Write the importance of normal distribution.
(c) If the mean and S.D of normal distribution are 70 and 16, find
p(x=38) < x [8+8]
1 of 2
Code No: RR220105 Set No. 1
4. To compare two kinds of bumper guards, 6 od each kind were monted on a car and
then the car has ran into a concrete wall. The following are the costs of repairs:
Guard1 107 148 123 165 102 119
Guard2 134 115 112 151 133 129
Use the 0.01 level of significance to test whether the difference between two sample
means is significant? [16]
5. (a) A sample of size 64 and mean 60 was taken from a population whose standard
deviation is 10. Find 95% confidence interval for the mean.
(b) Experience has shown that 10% of a manufactured product is of top quality.
What can you say about the maximum error with 95% confidence for 100
items
(c) A coin is tossed 512 times. Head turned up 244 times. Can you say that the
coin is unbiased. [5+5+6]
6. (a) A random sample from a company’s very extensive files shows that the orders
for a certain kind of machinery were filed, respectively in 10,12,19,14,15,18,11
and 13 days. Use the level of significance a=0.01 to test the claim that on the
average such orders are field in 10.5 days. Assume normality?
(b) The results of polls conducted 2 weeks and 4 weeks before a gubernatorial
election are shown in the following table:
Two weeks before election Four weeks before election
For Republican canditate 79 91
For Democratic canditate 84 66
Undecided 37 43
Use the 0.05 level of significance to test whether there has been a change in
opinion during the 2 weeks between the polls. [8+8]
7. (a) Derive normal equations to fit a parabola y = a0 + a1x + a2x2
(b) Fit the curve y = aebx for the following data [6+10]
x 1 5 7 9 12
y 10 15 12 15 21
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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