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R6-14-MCA-PROBABILITY-AND-STATISTICS-set1

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									      www.andhracolleges.com The Complete Information About Colleges in Andhra Pradesh


       Code No: R6-14-MCA                                                        R8-R6

               M.C.A. I Semester Regular Examinations, January 2009
                         PROBABILITY AND STATISTICS
                     Common to 2008, 07 and 06 Admitted Batches
       Time: 3 hours                                          Max Marks: 60
                            Answer any FIVE Questions
                           All Questions carry equal marks




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         1. (a) The probability that certain electronic component fails when first used is 0.10.
                If it does not fail immediately, the probability that it lasts for one year is 0.99.
                What is the probability that a new component will last for one year?
             (b) Three groups A, B, C are contesting for positions on the Board of Directors
                 of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively.
                 If the group A wins, the probability of introducing a new product is 0.7 and
                 the corresponding probabilities for group B and C are 0.6 and 0.5 respectively.
                 Find the probability that the new product will be introduced.

         2. If X is a continuous random variable and Y = aX + b prove that E(Y) = aE(X) +
            b and V(Y) = a2 V(X).

         3. Among the items produced in a factory 5% are defective. Find the probability that
            a sample of 8 contains.

             (a) Exactly 2 defective items




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             (b) Grater than or equal to 7 defective items
             (c) At least one defective item.

         4. If a 1 gallon can of point covers on the average 513.3 square feet with a std. deviation
            of 31.5 square feet. What is the probability that the mean area covered by a sample
            of 40 of these gallon cans will be anywhere from 510 to 520 square feets?

         5. (a) A Random sample of 100 items is taken from a population whose standard
                deviation is 5.1 The mean of the sample is 21.6. Construct 95% confidence
                interval for the mean
             (b) What is the maximum error one can expect to make with probability 0.9,
                 when using the mean of a random sample of size n=64 to estimate the mean
                 of a population with σ 2 = 2.56
             (c) A random sample of 400 flower stems has an average length of 15 cms. Can
                 this be regarded as a sample from a large population with mean 16 cms and
                 standard deviation 5 cms.?

         6. (a) Two independent random samples of sizes 100 and 120 have means 50 and 60
                with S.D. of 5 and 6. Construct 95% confidence interval for the difference of
                two means.
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       Code No: R6-14-MCA                                                          R8-R6
            (b) Random samples of 300 men and 500 women in a locality were asked whether
                they would like to have a fly over near their residence. 150 men and 200 women
                were in favour of the proposal. Test the significance between the difference of
                two proportions at 5% level.

         7. For the data given below use χ2 test to test the effectiveness of inoculation in
            preventing the attack of small pox.




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                                     Attacked Not attacked
               inoculate                25        220
             Not inoculated             90        160
                     σ 2 +σ 2 −σ 2
                        y
         8. Use r = x 2σx σy xy to find r for the following data and hence find the two lines of
            regression.


                              x 21 23 30 54 57 58 72 78 87 90
                              y 60 71 72 83 110 84 100 92 113 135




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