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Code No.220155

II-B.Tech. II-Semester Supplementary Examination January - 2003

b)

3.a)

b)

The mean weight of 500 male students at a certain college is 75 kg and the standard deviation is 7kg. Assuming that the weights are normally distributed. Find how many students weigh i) Between 60 and 78 kg ii) More than 92 kg. State and prove Chebyshev’s inequality. A population consists of the five numbers 2,3,6,8,11. Consider all possible samples of size two which can be drawn with replacement from this population. Find (a) The mean of the population (b) Standard deviation of the population (c) The mean of the sampling distribution of means (d) The standard error of means. Verify (c) and (d) directly from (1) and (2).

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Define Poisson process with example and show that mean = varience for a Poisson distribution. Given that f(x) = k/2x is a probability distribution for a random variable X, that can take on the values x = 0,1,2,3 and 4 (i) find k (ii) mean and varience of x.

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PROBABILITY AND STATISTICS (Common to Civil Engineering, Mechanical Engineering, Production Engineering, Computer Science and Engineering, Chemical Engineering, Computer Science and Information Technology, Mechanical Manufacturing Engineering and Mechatronics) Time:3 hours Max.Marks:70 Answer any FIVE questions All questions carry equal Marks --1.a) State three axioms of probability. b) Urn I has 2 white and 3 black balls. Urn II has 4 white and 1 black and Urn III has 3 white and 4 black. An Urn is selected at random and a ball is drawn at random is found to be white. Find the Probability that Urn I was selected.

5.a)

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b)

A sample poll of 100 voters chosen at random from all voters in a given district indicated that 55% of them were in favour of a particular candidate find 99%. Confidence limits for the proportion of all the voters in favour of this candidate. The IQ’s of 16 students from one area of a city showed a mean of 107 with a standard deviation of 10. While the IQ’s of 14 students from another area of the city showed a mean of 112 with a standard deviation of 8. Is there a significant differences between the IQ’s of the two groups at .01 level of significance.

(contd…2)

Code No.220155

b)

7.

OR

A sample of 900 members has a mean 3.4cms and standard deviation 2.61cms. Is the sample population of mean 3.25cms. and standard deviation 2.61cms? If the population is normal and its mean is unknown, find the 95% confidence limits. In a year there are 956 births in a town A, of which 52.5% were males, while in towns A and B combined this proportion in a total of 1,406 births was 0.496. Is there any significant difference in a proportion of male births in the two town? Find the least squares regression line of y on x and x on y. X 6 5 8 8 7 6 10 4 9 7 Y 8 7 7 10 5 8 10 6 8 6

Fit a Poisson distribution to the data and test the goodness of fit at 5% level of significance.

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X 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Y 0 20 43 53 86 70 54 37 18 10 5 2 2 0 0 0 0 ***

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Code No.220155 II-B.Tech. II-Semester Supplementary Examination ...

b) State and prove Chebyshev's inequality. 4. A population consists of the five numbers 2,3,6,8,11. Consider all possible · samples of size two which can be ...

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