Download JNTUA MCA 2019 May Reg-Supply 1st Sem 9FBS101 Probability And Statistics Question Paper

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Code: 9FBS101

MCA I Semester Supplementary Examinations May/June 2019

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PROBABILITY & STATISTICS

(For 2009, 2010, 2011, 2012 (LC), 2013, 2014, 2015 & 2016 admitted batches only)

Time: 3 hours Max. Marks: 60

Answer any FIVE questions

All questions carry equal marks

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1. Box A contains 5 red and 3 white marbles and box B contains 2 red and 6 white marbles. If a marble is drawn from each box, what is the probability that they are both of same colour.
2. In a factory, machine A produces 40% of the output and machine B produces 60%. On the average, 9 items in 1000 produced by A are defective and 1 item in 250 produced by B is defective. An item drawn at random from a day’s output is defective. What is the probability that it was produced by A or B?
3. Let X denote the number of heads in a single toss of four fair coins. Determine: (i) P(X<2). (ii) P(1<X<3).
4. Suppose a continuous random variable X has the probability density f(x) = k(1 - x*) for 0 < x < 1, and f(x) = 0 otherwise. Find: (i) k. (ii) Mean.
5. The mean and variance of a binomial distribution are 4 and 4/3 respectively. Find P(X > 1).

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6. In a sample of 1000 cases, the mean of certain test is 14 and standard deviation is 2.5. Assuming the distribution to be normal, find: (i) How many students score between 12 and 15? (ii) How many score above 18?
7. Let S ={1, 5, 6, 8}, find the probability distribution of sample mean for a random sample of size 2 drawn without replacement.
8. A random sample of size 100 has a standard deviation of 5. What can you say about the maximum error with 95% confidence?
9. A sample of 11 rats from a central population had an average blood viscosity of 9.32 with a standard deviation of 0.61. Estimate the 95% confidence limits for the mean blood viscosity of the population.
10. A sample of 64 students have a mean weight of 70 kgs. Can this be regarded as a sample from a population with mean weight 56 kgs and standard deviation 25 kgs?

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11. In a big city 325 men out of 600 men were found to be smokers. Does this information support the conclusion that the majority of men in this city are smokers?
12. A sample of 26 bulbs gives a mean life 990 hours with S.D of 20 hours. The manufacturer claims that the mean life of bulbs in 1000 hours. Is sample not up to the standard?
13. The number of automobile accidents per week in a certain community are as follows: 12, 8, 20, 2, 14, 10, 15, 6, 9, 4. Are these frequencies in agreement with the belief that accident conditions were the same during this 10 week period?
14. Fit a straight line to the data given below:
    X | 0 | 5 | 10 | 15 | 20 | 25
    

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    Y | 12 | 15 | 17 | 22 | 24 | 30
15. Calculate the regression equation of Y on X form the following data given bellow, taking deviations from actual means of X and Y.
    Price(Rs) | 10 | 12 | 13 | 12 | 16
    Demand | 40 | 29 | 42 | 45 | 27 | 42

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