Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R13 2018 June-July 811AD Probability And Statistics Previous Question Paper
R13
Code No: 811AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations June/July - 2018
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)
A class of 12 boys and 8 girls three students are selected at random one after the other.
Find the probability that i) first two are boys and third is girl ii) first and third are of the
same sex and the second is of opposite sex.
[4]
b)
In the month of September, on an average, rain falls on 10days. Find the probability:
i) that the rain fall on just two days of a given work, ii) that in three days of a given
week, it rains and the remaining four days it wont rain.
[4]
c)
Construct a 99% confidence interval for the true mean weight loss if 16 persons on diet
control after one month had a mean weight loss of 3.42 kgs with s.d. of 0.68kgs. [4]
d)
Test the claim of a manufacturer that 95% of his ,,stabilizers confirm to ISI specifications
if out of a random sample of 200 stabilizers produced by this manufacturer 18 were faulty.
Use 0.01 L.O.S.
[4]
e)
Show that the coefficient of correlation lies between -1 and 1.
[4]
PART - B
5 ? 8 Marks = 40
2.a)
The probabilities of passing in subject A,B,C and D are ?, 2/3, 4/5 and ? respectively.
To qualify in the examination a student should pass in A and two subjects among the three
what is the probability of qualifying in that examination.
b)
A card is drawn from a well shuffled pack of cards, if the card shows up red, one die is
thrown and the result is recorded but if the card shows black two dies are thrown and their
sum is recorded. What is the probability that the recorded number will be 2?
[4+4]
OR
3.a)
Two sets of candidates competing for the positions of the board of directors of a company.
The probability that the first and second set will win are 0.6 and 0.4 respectively. If the
first set wins the probability of introducing a new product is 0.8 and the corresponding
probability in the second set wins is 0.3 what is the probability that the new product will
be introduced.
b) If E1, E2, E3 are mutually independent events of a sample space S, then E1 U E2 and E3 are
also independent events.
[4+4]
4.a)
A continuous random variable has the PDF = 2-2 > 0 . Find the
0
probabilities that it will take on a value i) between 1 and 3 ii) greater than 0.5.
b)
A car hire firm has two cars which it hires out day by day. The number of demands for a
car on each day is distributed as Poisson variant with mean 1.5. Calculate the proportion
of days on which i) Neither car is used ii) Some demand is refused.
[4+4]
OR
5.
The income of a group of 10,000 persons was found to be normally distributed with mean
Rs.750 p.m. and standard deviation Rs.50. Show that of this group about 95% had income
exceeding Rs.668 and only 5% had income exceeding Rs.832. What was the lowest
income among the richest 100?
[8]
6.
A Professors feeling about the mean mark is the final examination in "probability" of a
large group of students is expressed subjectively by normal distribution with 0 = 67.2 and
0 = 1.5. a) If the mean mark lies in the interval (65.0, 70.0) determine he prior
probability the professor should assign to the mean mark. b) Find the posterior mean 1
and posterior s.d. 1= if the examination is conducted on a random sample of 40 students
yielding mean 74.9 and s.d. 7.4. Use s = 7.4 as an estimate of . c) Determine the
posterior probability which he will thus assign to the mean mark being in the interval (65,
70), using results obtained is (b) and (c) construct a 95% Bayesian interval for . [8]
OR
7.
A population consists of five numbers 3, 4, 5, 6, 7. Consider all possible district samples
of size three without replacement. Find a) the population (S.D) mean b) the population
standard deviation (s.d.) c) the sampling distribution of means d) the mean of the S.D. of
means e) standard deviation. of S.D. of means. Verify (c) and (e) directly from (a) and
(b) by use of suitable formulae.
[8]
8.a)
Is there reason to believe that the life expected in south and north India is same or not
from the following data
South 34
39.2 46.1 48.7 49.4 45.9 55.3 42.7 43.7
North 49.7
55.4 57
54.2 50.4 44.2 53.4 57.5 61.9 56.6 5
b)
A machine runs on an average of 125 hours/year. A random sample of 49 machines has
an annual average use of 126.9 hours with standard deviation 8.4 hours. Does this suggest
to believe that machines are used on the average more than 125 hours annually at 0.05
level of significance?
[4+4]
OR
9.a)
The heights of 6 randomly chosen sailors are (in inches) 63, 65, 68, 69, 71 and 72. Those
of 9 randomly chosen soldiers are 61, 62, 65, 66, 69, 70, 71, 72 and 73. Test whether the
sailors are on the average taller than soldiers.
b)
The sales in a supermarket during a week as given below. Test the hypothesis that the
sales do not depend on the day of the week, using a significant level of 0.05.
Days
:
Mon Tues Wed
Thurs Fri Sat
Sales (in 1000Rs):
65
54 60
56
71 84
[4+4]
10.a) Find if there is any significant correlation between the heights and weights given below
Heights in inches
57
59
62
63
64
65
55
58
57
Weights in lbs 113
117
126
126
130
129
111
114
112
b) If the two regression lines of y on x and x on y are respectively a1x + b1y + c1 = 0 and
a2x + b2y + c2 = 0 prove that a1b2 < a2b1.
[4+4]
OR
11.
The following are the marks obtained by 132 students in test X and test Y
X\Y
30-40
40-50
50-60
60-70
70-80
Total
20-30
2
5
3
10
30-40
1
8
12
6
27
40-50
5
22
14
1
42
50-60
2
16
9
2
29
60-70
1
8
6
1
16
70-80
2
4
2
83
Total
3
21
63
39
6
132
Calculate: a) The correlation coefficient b) The regression equation.
[8]
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This post was last modified on 16 March 2023