Download AKTU B-Tech 3rd Sem 2016-2017 NCE 30 Surveying I Question Paper

II B.Tech I Semester Regular Examinations, December 2017/January 2018

PROBABILITY AND STATISTICS

(Com. to CE, CSE, IT)

Time: 3 hours Max. Marks: 70

Note: 1. Question Paper consists of two parts (Part-A and Part-B)

2. Answer ALL the question in Part-A

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3. Answer any FOUR questions from Part-B

PART-A

1. a) Define Random variable and mathematical expectation. (2M)

b) Write the properties of normal distribution. (3M)

c) Define null hypothesis and alternative hypothesis. (2M)

d) Define type-I and type-II errors. (3M)

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e) Write about the properties of queuing system. (2M)

f) Define transient and steady state. (3M)

PART-B

2. a) A random variable X has the following probability function:

Determine (i) k (ii) Evaluate P(X<6), P(X=6) (iii) Evaluate P(0 (7M)

b) Average number of accidents on any day on a national highway is 1.6. Determine the probability that the number of accidents are (i) at least one (ii) at most one. (7M)

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3. a) In a normal distribution, 7% of the items are under 35 and 89% are under 63. Determine the mean and variance of the distribution. (7M)

b) If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random (i) 1 (ii) 0 (iii) at least 2 bolts will be defective. (7M)

4. a) A population consists of the four numbers 3, 7, 11, 15. Consider all possible samples of size 2 which can be drawn without replacement from the population. Find the population mean and standard deviation, and mean and standard deviation of the sampling distribution of means. (7M)

b) The mean life time of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If µ is the mean lifetime of all the bulbs produced by the company, test the hypothesis µ = 1600 hours, against the alternative hypothesis µ ? 1600 hours, using a 5% level of significance. (7M)

5. a) Two independent samples of sizes 9 and 8 from two normal populations gave the following values:

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Test whether the two populations have the same variance. (7M)

b) The following are the number of mistakes made in 4 successive weeks by 4 technicians working for a telephone company:

Test at the 0.05 level of significance whether the difference among the sample means can be attributed to chance. (7M)

6. a) Fit a Poisson distribution to the following data and test the goodness of fit:

(7M)

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b) A die is thrown 264 times with the following results. Show that the die is biased.

(7M)

7. a) Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The length of phone call is assumed to be distributed exponentially with mean 3 minutes.

(i) What is the probability that a person arriving at the booth will have to wait?

(ii) What is the average length of queues that form from time to time?

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(7M)

b) Assume that at an average 3 customers per hour arrive at a single window drive in bank. Assume also that it takes an average of 5 minutes to serve each customer. What is the probability that the waiting line length is more than 2? (7M)

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