Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R13 2017 August 811AD Probability And Statistics Previous Question Paper
R13
Code No: 811AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, August - 2017
PROBABILITY AND STATISTICS
Time: 3hrs
Max.Marks:60
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 20 marks. Answer all questions in Part A.
Part B consists of 5 Units. Answer any one full question from each unit. Each
question carries 8 marks and may have a, b, c as sub questions.
PART - A
5 ? 4 Marks = 20
1.a)
There are 12 cards numbered 1 to 12. If two cards are selected, what is the probability
that the sum is odd, if the cards are drawn.
i) With replacement
ii) Without replacement.
[4]
b)
The mean and variance of binomial distribution are 4 and 4/3 respectively. Find P(x 1).
[4]
c)
The S.D of a population is 140.5 and the sample size 50. Find the maximum error with
95% confidence.
[4]
d)
The nicotent content in milligrams of two samples of tobacco were given in the following
table. Find the standard error for the difference between the means at 5% level.
[4]
Sample A
24
27
26
23
25
Sample B
29
30
30
31
24
36
e)
The equations of two regression lines obtained in a correlation analysis are
3x + 12 y = 19, 3y + 9x = 46. Find
i) Coefficient of Correlation ii) The means of x and y.
[4]
PART - B
5 ? 8 Marks = 40
2.a)
If A and B are two events and P(A) = 3/5 and P(B) = 1/ 2, then
Prove that
i) P(A B) 3 / 5
ii) 1 / 10 P(A B) 1 / 2
b)
A purse contains 2 silver and 4 copper coins and a second purse contains 4 silver and
4 copper coins. A coin is selected from one of the purses are found that it is copper coin.
Find the probability that it is i) From purse I ii) From purse-II.
[4+4]
OR
3.a)
What is the probability of getting two queens, if we draw two cards from a pack of 52
cards.
i) With replacement
ii) Without replacement.
b) In a certain college 25% of the students failed in mathematics, 15 % failed in chemistry.
A student is selected at random.
i) If he failed in Mathematics, what is the probability that he failed in Chemistry.
ii) If he failed in Chemistry, what is the probability that he failed in Mathematics. [4+4]
4.a)
The probabilities of a Poisson, variate taking the values 1 and 2 are equal.
Find i) ?
ii) P(x1)
b)
In a sample of 1000 cases, the mean of a certain test is 14 and standard deviation is 2.5.
Assuming the distribution to be normal, find how many students score between
12 and 15.
[4+4]
OR
5.
The probability that the life of a bulb is 100- days is 0.05. Find the probability that out of
6 bulbs
a) At least one
b) None will have a life of 100 days.
[4+4]
6.a)
A sample of size 81 was taken whose variance is 20.25 and mean 32. Construct 95%
confidence interval for the mean.
b)
The standard deviation of heights of students is 10 cms. A sample of 196 students was
taken and the mean is 170 cms. Is this sample has been taken from a large population
whose mean is 175 cms?
[4+4]
OR
7.
Random samples of 600 men and 900 women in a locality were asked whether they
would like to have a bus stop near their residence .350 men and 475 women were in
favour of the proposal. Test the significance between the difference of two proportions at
5% level.
[8]
8.
Four methods are under development for making discs of a super conducting material.
Fifty discs are made by each method and they are checked for super conductivity when
coloid with liquid nitrogen.
Method-I
Method-II Method-III Method-IV
Super
31
42
22
25
Conductor
Failures
19
8
28
25
Perform a Chi-square test at 0.05 level whether there is a significance difference between
the proportions.
[8]
OR
9.
To compare the prices of a certain product in two cities, ten shops were selected at
random in each town. The prices noted are given below
City I
75
89 96 101 104 110 120 123 114 115
City II 115
75 87 96
89
96
97
105 104 115
Test whether the average prices can be said to be same in the two cities.
[8]
10.
Fit an equation of the form y = abx to the following data
x
2
3
4
5
6
y 144 172.8 207.4 248.8 298.5
[8]
OR
11.
The marks obtained by 10 students in Mathematics and Statistics evaluated for 50 marks
are given below. Find the Coefficient of Correlation between the two subjects.
[8]
Marks in Maths
25
28
30
32
35
36
38
39
42
45
Marks in Statistics
20
26 29
30
25
18
26
35
35
46
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This post was last modified on 16 March 2023