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Posted By: kondapalli Member Level: Gold Posted Date: 05 Jul 2008
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2007 Jawaharlal Nehru Technological University B.Tech Metallurgy & Material Technology PROBABILITY AND STATISTICS setno 2 Question paper
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1. (a) A Band C in order toss a coin. The first one to toss a head wins the game.
What are their probabilities of winning, assuming that the game may continue
indefinitely?
(b) State and prove Baye’s theorem. [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) Define Poisson distribution and find its variance and the mean.
(b) Find the mean and standard deviation of a normal distribution in which 7%
of items are under 35 and 89% are under 63. [8+8]
4. A population consists of 5,10,14,18,13,24 consider all possible samples of size two
which can be drawn without replacement from the population. Find
(a) The mean of the population.
(b) The standard deviation of the population.
(c) The mean of the sampling distribution of means
(d) The standard deviation of sampling distribution of means. [4X4]
5. (a) In a random sample of 125 cola drinkers, 68 said they prefer thums up to
pepsi. Test the null hypothesis p = .5 against the alternate hypothesis p>.5
(b) A random sample of 100 teachers in a large metropolitan area revealed a mean
weekly salary of Rs. 487 with a standard deviation Rs. 48. With what degree
of confidence can we assert that the average weekly salary of all teachers in
the metropolitan area is between 472 to 502? [8+8]
6. (a) The following data gives the fields of interest and attitude to religion:
Arts & Commerce Science & Engineering Total
Conformist 109 51 160
Non-Conformist 23 17
Total 132 68 200
Examine whether the field of interest and attitude to religion are associated.
(b) Assuming tht s = 20.0, how large a random sample be taken to assert with
probability 0.95 that the sample mean will not differ from the true mean by
more than 3.0 points? [16]
1 of 2
Code No: RR311801 Set No. 2
7. (a) Derive normal equations to fit a parabola y = a0 + a1x + a2x2
(b) Fit the curve y = aebx for the following data
x 1 5 7 9 12
y 10 15 12 15 21
[6+10]
8. Find the least sequences regression equation of x1onx2andx3 from the following
data.
X1 3 5 6 8 12 14
X2 16 10 7 4 3 2
X3 90 72 54 42 30 14
[16]
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