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Posted By: murali Member Level: Silver Posted Date: 28 Apr 2008
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2007 Jawaharlal Nehru Technological University B.Tech Mechanical Engineering PROBABILITY AND STATISTICS SET NO 1 Question paper
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Code No: R05220101 Set No. 1
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 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 solv-
ing 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) Let X denote the minimum of the two numbers that appear when a pair of
fair dice is thrown once. Determine the
i. discrete probability distribution
ii. expectation
iii. variance.
(b) Show that if p is small and n is large, then the binomial distribution B(n,p)
is approximated by the Poisson distribution. [8+8]
3. (a) If a Poisson distribution is such that P(x=1). 3
2 = P(x=3).
Find
i. p(x 1)
ii. p(x 3)
iii. p(2 x 5)
(b) A sales tax officer has reported that the average sales of the 500 business that
he has to deal with during a year is Rs.36,000 with a standard deviation of
10,000. Assuming that the sales in these business are normally distributed,
find
i. the number of business as the sales of while are Rs.40,000
ii. the number of business the sales of while are likely to range between Rs.
30,000/- and Rs.40,000/- [8+8]
4. If the population is 3,6,9,15,27.
(a) List all possible samples of size 3 that can be taken without replacement from
the finite population.
(b) Calculate the mean of each of the sampling distribution of means.
1 of 2
Code No: R05220101 Set No. 1
(c) Find the standard deviation of sampling distribution of means. [5+5+6]
5. (a) A sample of size 36 was drawn and its mean was found to be 80. Test whether
this sample could have come from a normal population with mean 90 and
variance 225?
(b) A die is thrown 1350 times 5 or 6 obtained 650 times test whether the die is
unbiased. [8+8]
6. Suppose during 400 five- minute intervals the ari-traffic control of an airport re-
ceived 0, 1,.........,12 messages and observed frequencies are given in the following
table.
No.of Messages
x 0 1 2 3 4 5 6 7 8 9 10 11 12
f 4 15 47 76 68 74 46 39 15 9 5 2 0
Test whether the Poisson distribution with ? = 4.5 provides a good fit to the above
data? [16]
7. (a) The measurements of humidity and the moisture content in a raw material
are given in the following table. Fit a St. line of the for y = ax + b Humidity
(x)
42 35 50 43 48 62 31 36 44 39 55 48
12 8 14 9 1 16 7 9 12 10 13 11
(b) Find the most plausible values of x and y
x + 2y - 7 = 0 2x + 3y - -2 = 0
x + 8y - 3 =0 3x - y + 5 = 0. [8+8]
8. The following data relate to the marks of 10 students in the internal test and the
university examination for the maximum of 50 each
Internal marks (x) 25 28 30 32 35 36 38 39 42 45
University marks (y) 20 26 29 30 25 18 26 35 35 46
Find the coefficient of correlation and the two lines of regression. [16]
? ? ? ? ?
2 of 2
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