Code No:220155 II-B.Tech. II-Semester Examinations, April/May, 2003

OR

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PROBABILITY AND STATISTICS (common to Civil Engineering, Mechanical Engineering, Production Engineering, Mechanical and Manufacturing Engineering, Computer Science and Engineering, Chemical Engineering, Computer Science and Information Technology, Mechatronics)

1.a)

b)

Max. Marks:70 Answer any FIVE questions All questions carry equal marks --A and B throw alternately with a pair of ordinary dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A begins, show that his chance of winning is 30/61. Suppose 5 men out of 100 and 25 women out of 10,000 are colour blind. A colour blind person is chosen at random. What is the probability of the person being a male? (Assume male and female to be in equal numbers).

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Time: 3 hours

In a bolt factory, P, Q and R manufacture 25%, 35% and 40% of the total. Of their output 5%, 4% and 2% are defective bolts. A bolt is drawn at random from the product and found to be defective. What are the probabilities that it was manufactured by machines P, Q or R?

3.a)

If X is a continuous random variable with pdf given by f(x) = kx if 0  x < 2 = 2k if 2  x < 4 = -kx + 6k if 4  x < 6. Find k and mean value of X. In 256 sets of 12 tosses of a coin, in how many cases one can expect eight heads and 4 tails?

b)

A process for making certain bearings is under control if the diameters of the bearings have the mean of 0.5000 cm. What can we say about this process if a sample of 10 of these bearings has a mean diameter of 0.5060 cm and a standard deviation of 0.0040 cm? Prove that the variance of a sample of n numbers a, a + d, a + 2d ….. a + (n-1) d is

nt

4.a)

uW

2.

1 2  n 1d 2 . 12

Aj

b)

given by

Contd…..2

Code No:220155

b)

OR

The average sale of a toilet soap in a particular locality in a particular shop is an average 320 and S.D 40. An attractive display of advertisement for the soap in local TV increased in 36 days the sale by 70 in that soap in a day. Can we say that the advertisement has helped very much? A company manufacturing electric bulbs claims that the average life of its bulbs is 1600 hours. The average life and standard deviation of a random sample of 100 such bulbs were 1570 hours and 120 hours respectively. Should we accept the claim of the company?

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5.a)

-2-

A random sample of 6 steel beams has a mean compressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and level of significance α = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. (8)

b)

Measurements of the fat content of two kinds of ice cream, Brand A and Brand B, yielded the following sample data:

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6.a)

Brand A (%) 13.5 14

13.6 12.9 13

Brand B (%) 12.9 13

12.4 13.5 12.7

7.

uW

Test the null hypothesis μ1 = μ2 (where μ1 and μ2 are the respective true average fat contents of the two kinds of ice cream) against the alternative hypothesis μ1≠ μ2 at the level of significance α =0.05. Fit an exponential curve of the y= AeBX for the following data x y

2 11

3 17

4 27

Find the rank correlation for the following data.

nt

8.

1 7

56 147

42 125

Aj

x y

72 160

36 118

63 149

47 128 ---

55 150

49 145

38 115

42 140

68 60 152 155