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Posted Date: 26 Jun 2008 Posted By: Sunil Reddy Member Level: Platinum
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2007 Jawaharlal Nehru Technological University Chemical engineering II B.Tech II Semester Regular Examinations, Apr/May 2007 PROBABILITY AND STATISTICS Question paper
Set No. 2
II B.Tech II Semester Regular Examinations, Apr/May 2007
PROBABILITY AND STATISTICS
( Common to Civil Engineering, Mechanical Engineering, Chemical
Engineering, Mechatronics, Production Engineering, Bio-Technology and
Automobile Engineering)
Time: 3 hours
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
Max Marks: 80
1. (a) Two marbles are drawn in succession from a box containing 10 red, 30 white, 20
blue and 15 orange marbles, with replacement being made after each drawing..
Find the probability that
i. both are white
ii. ?rst is red and second is white
(b) A businessman goes to hotels X,Y,Z 20%, 50%, 30% of the time respectively. It
is known that 5%, 4%, 8% of the rooms in X,Y,Z hotels have faulty plumbing.
What is the probability that business mans room having faulty plumbing is
assigned to hotel Z.
[8+8]
2. (a) If X and Y are discrete random variables and K is a constant then prove that.
i. E ( X + K) = E(X) + K
ii. E(X+Y) = E(X) + E(Y)
(b) Out of 800 families with 5 childrens each, how many would you expect to have
i. 3 boys
ii. At least one boy.
3. (a) Find the mean of the normal distribution .
[8+8]
(b) Suppose the weights of 800 male students are normally distributed with mean
=140 pounds and standard deviation 10pounds. Find the number of students
whose weights are
i. between 138 and 148pounds
ii. more than 152pounds
[8+8]
4. Take 30 slips of paper and label 5 each -4 and 4, four each - 3 and 3, three each -
2 and 2 and each-1, 0 and 1, if each slip of the paper has the same probability of
being drown ?nd the probabilities of getting - 4,- 3, - 2, - 1, 0, 1, 2, 3, 4 and ?nd
the mean and varience of this distribution of means.
[16]
5. (a) A sample of size 64 and mean 60 was taken from a population whose standard
deviation is 10. Find 95% con?dence 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% con?dence for 100
items
1 of 2
Code No: R05220101
Set No. 2
(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) To examine the hypothesis that the husbands are more intelligent than the
wives, an investigator took a sample of 10 couples and administered them a
test which measures the IQ as follows:
Test the hypothesis with a reasonable test at the level of signi?cance of 0.05?
Husbands: 117 105 97 105 123 109 86 78 103 107
Wives
106 98 87 104 116 95 90 69 108 85
(b) In an investigation on the machine performance the following results were
obtained:
No.of Units inspected No. of defectives
Machine 1
Machine 2
375
450
17
22
Test whether there is any signi?cant performance of two machines at a=0.05
[8+8]
7. (a) Fit a curve of the form y = aebxfor the following data
x 0.0 .5 1.0 1.5 2.0
2.5
y .1 .45 2.15 9.15 40.35 180.75
(b) Find the most plausible values of x and y from the following equations x + 2y
= 6, 2x - y = 2, 2x - 5y = 7, 3x - 4y = - 4
[8+8]
8. (a) The following table gives experimental values of the three variates X,Y and Z.
Fit a multiple regression of the type Z = a X + ßY.
X 1 2 3 5
Y 1 3 4 2
Z 7 18 25 23
(b) The following are the marks obtained by 12 students in Economics and Sta-
tistics:
Economics(x) 78 56 36 66 25 75 82 62
Statistics(y) 84 44 51 58 60 68 62 58
Compute the Spearman rank correlation coe?cient between x and y. [8+8]
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