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

Code No: 21004
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA-I Semester Supplementary exams July/August 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 mutually exclusive events such that P(A) = four P(B) and
A ? B = S. obtain
i) P(A nBC ).
ii) P( AnB)
iii) P( AC ?B)
b) A box I contains three red balls,2 black and one white balls. Box II contains one red, one black
ball and three white balls, Box III contains three red, three black balls and three white balls. A box is
chosen at random and a ball is drawn, if it is from box I, what is the probability that it is
i) Red ii) Black iii) White
2. a ) A continuous Random variable has the p.d.f f(x)=Kxe -?x , if x=0, ? =0
=0 otherwise
Determine i) K ii) The mean iii) variance.
b) A learner takes a actual false exam consisting of eight ques.. He guesses every
answer. The guesses are made at random. obtain the smallest value of n that the
probability of guessing at lowest n accurate answers is less than one / 2.
3. a) If the variance of a Poisson variate is 3. obtain the probability that
i) P(x=0) ii) P(1=x<4) iii) P( x > 2)
b) 800 students appear for an exam. It was obtained that the marks are normally
distributed with mean 60 and standard deviation 12. The students who get more than or
equal to 60 will be placed in first division, who get ranging from 50 and 60 will be placed in
2nd division, who get ranging from 40 and 50 in third division, who get more than 75 in
distinction and who get less than 40 will be failed. obtain the number of students who get
i)1st division ii) third division iii) Failed
4. a) A sample of 50 items is taken from a population whose standard deviation is 12. The
mean of the sample is 68. Construct 95% confidence interval.
b) A random sample of size 225 is taken whose mean is 80. Can this be regarded as a
sample from a population with mean weight 82 and standard deviation 15.
5.a) Write about critical region and level of significance.
b) During a countrywide investigation the incidence of tuberculosis was obtained to be 3%
in a college 700 strength. five reported to be effected in a different sample of 1000
strength. Test the significance ranging from the difference of 2 proportions at 5%
level.
Cont…2
6. 200 digits were chosen at random from a set of tables. The frequencies of the digits
are
digits 0 one two three four five six seven eight 9
Frequency 18 19 23 21 16 25 22 20 21 15
Use ? two test to assess the correctness of hypothesis that the digits were distributed in
equal numbers in the table.
7. compute the coefficient of correlation and the 2 lines of regression ranging from the
two variables x and y.
8. a) Write about components of Time series.
b) Write about characteristics of control charts.
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x 14 16 17 18 19 20 21 22 23
y 84 78 70 75 66 67 62 58 60
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