Categories: Second Year Second Semester (2-2)

Code No: RT22051

II B. Tech II Semester Supplementary Examinations, April-2018

PROBABILITY AND STATISTICS (Com. to CSE, IT, CHEM, PE, PCE)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

3. Answer any THREE Questions from Part-B

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART-A

1. a) if X is a normal variate then Find (i) P(z
b) The mean and variance of binomial distribution are 4 and 3 respectively.

Find .

c) Explain the stratified sampling with a suitable example.

d) A random sample of size 100 has S.D of 5 .what is the maximum error with 95%confidence

e) Write about major classification of correlation?

f) What is the use of control charts? Draw a typical control chart. (4M+4M+3M+4M+3M+4M)

PART-B

2. a) The probability density function of a variate X is

X 0 1 2 3 4 5 6

P(X) K 3K 5K 7K 9K 11K 13K (i) Find P(x0.3

b) In a test on 2000 electric bulbs, it was found that the life of a particular make was

normally distributed with average life of 2040 hours and S.D of 60 hours . Estimate the

number of bulbs likely to burn for

i) More than 2150 hours,

ii) Less than 1950 hours and

iii) More than 1920 hours and but less than 2160 hours. (8M+8M)

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Code No: RT22051

II B. Tech II Semester Supplementary Examinations, April-2018

PROBABILITY AND STATISTICS (Com. to CSE, IT, CHEM, PE, PCE)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

3. Answer any THREE Questions from Part-B

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART-A

1. a) if X is a normal variate then Find (i) P(z
b) The mean and variance of binomial distribution are 4 and 3 respectively.

Find .

c) Explain the stratified sampling with a suitable example.

d) A random sample of size 100 has S.D of 5 .what is the maximum error with 95%confidence

e) Write about major classification of correlation?

f) What is the use of control charts? Draw a typical control chart. (4M+4M+3M+4M+3M+4M)

PART-B

2. a) The probability density function of a variate X is

X 0 1 2 3 4 5 6

P(X) K 3K 5K 7K 9K 11K 13K (i) Find P(x0.3

b) In a test on 2000 electric bulbs, it was found that the life of a particular make was

normally distributed with average life of 2040 hours and S.D of 60 hours . Estimate the

number of bulbs likely to burn for

i) More than 2150 hours,

ii) Less than 1950 hours and

iii) More than 1920 hours and but less than 2160 hours. (8M+8M)

1 of 2

R13

SET – 2

R13

SET – 1

Code No: RT22051

3. a) Calculate E(X),E(X

2

), from the distribution given below.

X 1 2 3

P(X) 1/5 3/10 1/2

b) Define Moment generating function and its properties. (8M+8M)

4. a) A random samples of size 25 from a normal population has the mean = 47.5 and the

standard deviation is equal to 8.4. Does this information tend to support or refute the claim

that the mean Of population is ?=42.5

b) Three masses are measured as 62.34,20.48,35.97kgs with S.D 0.54,0.21,0.46 kgs

respectively. Find mean and standard deviation of the sum of the masses (8M+8M)

5. a) Two independent samples of 8 and 7 items respectively has the following values

Sample1 11 11 13 11 15 9 12 14

Sample2 9 11 10 13 9 8 10 —-

Is the difference between the mean of samples significant?

b) A sample of 26 bulbs gives a mean life of 990 hours with a S.D of 20 hours.

The manufacturer claims that the mean life of bulbs is 1000 hours is the sample not up to the

standard. (8M+8M)

6. a) Calculate Karl Pearson?s correlation coefficient for the following paired data.

X 28 41 40 38 35 33 40 32 36 33

Y 23 34 33 34 30 26 28 31 36 38

b) Fit a parabola of the form y=a+bx+cx

2

to the following data (8M+8M)

x 1 2 3 4 5 6 7

y 23 5.2 9.7 16.5 29.4 35.5 54.4

7. Construct a control chart for men and the range for the following data on the basis of fuses,

sample of being taken every hour ( each set of 5 has been arranged in ascending order of

magnitude). Comment on whether the production seems to be under control, assuming that

these are the first data.

42 42 19 36 42 51 60 18 15 69 64 61

65 45 24 54 51 74 60 20 30 109 90 78

75 68 80 69 57 75 72 27 39 113 93 94

78 72 81 77 59 78 95 42 62 118 109 109

87 90 81 84 78 132 138 60 84 153 112 136

(16M)

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