Jawaharlal Nehru Technological University, Hyderabad M.C.A - I Semester Supplementary Examinations July 2010 PROBABILITY AND STATISTICS Question paper

Code No: 14

Time: 3hours Max.Marks:60

Answer any Five questions

All questions carry equal Marks

- - -

1. a) If A and B are two events, prove that P(A nB) = P(A) = P(A ?B) = P(A) +P(B)

b) Three machines I, II and III produce 25%, 35% and 40% of the total number of items of a factory. The percentages of defective items of these machines are 6%, 5% and 4%. An item is selected at random and found to be defective. Find the probability that it is from

i) Machine- I

ii) Machine-II

iii) Machine-III

2. a) Explain i) Random variable

ii) The probability distribution function.

b) Out of 2000 families with 400 each find the number of families having

i) At least one boy

ii) Exactly 2 boys

iii) 1 or 2 boys

3. a) If 3% of light bulbs are defective. Find

i) At least one is defective.

ii) Exactly 5 are defective

iii) P( 1< x < 5) in a sample of 100

b) Suppose the weights of 600 male students are normally distributed with mean µ =70 kgs with a standard deviation of 12. Find the number of students whose weights are

i) Between 65 and 88

ii) Greater than 90

4. a) A random sample of size 225 is taken from an infinite population having the mean 55 and the Standard deviation 15. What is the probability that

x will be between 48 and 82?

b) A random sample of size 97 is taken from an infinite population with the standard deviation 5. Find

i) The standard error

ii) Probable error

Cont…2

5. a) A random sample of size 61 was taken whose S.D is 4.5 and the mean is 20.

Construct 98% confidence interval for the mean.

b) What is the maximum error with 99% confidence, if the standard deviation of the sample of size 72 is 5?

c) A sample of 100 students is found to have a mean height of 160 cms. Can this be regarded as a sample from a population with mean weight 165 cms and standard deviation 25 cms.

6. a) In a city A 20% of a random sample of 900 school boys had a certain slight physical defect. In another city B 18.5% of a random sample of 1600 school boys had the same defect. Is the difference between the proportions is significant at .05 level of significance.

b) Samples of students were drawn from two universities and from their weights in kgm and deviations are calculated. Make a large sample test to test the significance of the difference between the means.

7. Fit a Poisson distribution to the following data and test the Goodness of Fit at.05

level of significance.

8. Use r =

2 2 2

2

x y xy

x y

s s s

s s

+ -

to find r for the following data and hence find the two lines

of regression.

*******

x 0 1 2 3 4 5 6

f 275 72 30 7 5 2 1

x 21 23 30 54 57 58 72 78 87 90

y 60 71 72 83 110 84 100 92 113 135