Download JNTUH MCA 1st Sem R09 2020 January F3104 Probability And Statistics Question Paper

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Code No: F3104 R09

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

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Answer any five questions
All questions carry equal marks

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1. a) There are 25 cards numbered 1 to 25. Two cards are drawn. Find the probability that their sums is 1) even i) a multiple of 3.
   b) There are three boxes. I contains- 10 light bulbs out of which 4 are defective II, contains- 6 light bulbs out of which 1 is defective, III contains- 8 light bulbs out of which 3 are defective. A box is chosen at random and a bulb is selected. If it is defective then find the probability that it is from:
   1) Box-1 i1) Box-II ii1) Box-III [6+6]
2. a) A random variable X has the following distribution
   X 1 1213 (4 |5
   

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   P(X=x) [1]1]1]1]1
   2|4 ]8]16]16
   Find: 1) The mean i1) variance. ii1) P(1< X< 4)
3. b) The probability of man hitting a target is 1/3. If he fires 6 times, find the probability of hitting: 1) At the most 5 times ii) At least 5 times ii1) Exactly once. [6+6]
4. b) Average number of accidents on any day on a national highway is 1.6. Determine the probability that the number of accidents is 1) at least one ii) at the most one

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5. b) The marks obtained by 1000 students is normally distributed with mean 78 % and Standard deviation 11%. Determine
   1) How many get more than 90%.
   i1) How many students get between 75% and 90%. [6+6]
6. a) A population consists of five numbers 5,10,15,20 .Consider all Samples of size two which can be taken with replacement from this population. Find:
   a) The population mean:
   

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   b) The population Standard deviation.
   c) The mean of the sampling distribution of means.
   d) Standard deviation of the sampling distribution of means. [12]
7. b) 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.
8. b) A sample of 121 students is found to have a mean weight of 68 kgs. Can this be regarded as a sample from a population with mean weight 75 kgs and standard deviation 31 kgs? [6+6]

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9. a) A simple sample of heights of 6400 Englishmen has a mean of 67.85 and Standard deviation of 2.56 inches. While a simple sample of heights of 1600 Australian has a mean of 68.55 and a S.D. of 2.52 inches Test the significance between the two mean.
10. b) 400 articles from a factory are examined and 3% are found to be defective. 600 similar articles from a second factory are found to be 2 % defective. Test the significance between the differences of two proportions at 5% level.
11. b) Two random sample are drawn from two normal populations are as follows.
    Sample I |17 |27 |18(25(27(29|13 |17
    SampleII |16 | 16]20[27[26]25]|21
    

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    Test whether two populations have been drawn from the same normal population. [12]
12. b) The marks obtained by 10 students in Mathematics and Statistics are given below. Find the Coefficient of correlation between the two subjects and the regression lines.
    Marks in Maths 75 130 |60 |80 |53 |35 [15 [40 |38 |48
    Marks in Statistics 85 |45 |54 |91 |38 |63 |35 (43 (45 |44

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