Jawaharlal Nehru Technological University Hyderabad 2010-1st Sem M.C.A -ester Supplementary s PROBABILITY AND STATISTICS - Question Paper

Code No: 14
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA-I Semester Supplementary exams July 2010
PROBABILITY AND STATISTICS
Time: 3hours Max.Marks:60
ans any 5 ques.
All ques. carry equal Marks
- - -
1. a) If A and B are 2 events, prove that
P(A nB) = P(A) = P(A ?B) = P(A) +P(B)
b) 3 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 opted at random and obtained to be defective. obtain the
probability that it is from
i) Machine- I
ii) Machine-II
iii) Machine-III
2. a) discuss i) Random variable
ii) The probability distribution function.
b) Out of 2000 families with 400 every obtain the number of families having
i) At lowest 1 boy
ii) Exactly two boys
iii) one or two boys
3. a) If 3% of light bulbs are defective. obtain
i) At lowest 1 is defective.
ii) Exactly five 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. obtain the number of students whose
weights are
i) ranging from 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 ranging from 48 and 82?
b) A random sample of size 97 is taken from an infinite population with the
standard deviation 5. obtain
i) The standard fault
ii) Probable fault
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 fault with 99% confidence, if the standard deviation of
the sample of size 72 is 5?
c) A sample of 100 students is obtained 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 a different city B 18.5% of a random sample of 1600 school boys
had the identical defect. Is the difference ranging from the proportions is significant at .05
level of significance.
b) Samples of students were drawn from 2 universities and from their weights
in kgm and deviations are computed. Make a large sample test to test the
significance of the difference ranging from the means.
7. Fit a Poisson distribution to the subsequent data and test the Goodness of Fit at.05
level of significance.
8. Use r =
2 two 2
2
x y xy
x y
s s s
s s
+ -
to obtain r for the subsequent data and hence obtain the 2 lines
of regression.
*******
x 0 one two three four five 6
f 275 72 30 seven five two 1
x 21 23 30 54 57 58 72 78 87 90
y 60 71 72 83 110 84 100 92 113 135

Earning:   Approval pending.