BBA
SECOND YEAR THIRD SEMESTER EXAMINATION, 2012
—––—–
BUSINESS
STATISTICS-II
SUBJECT
CODE: 2105
Time—3 hours
Full marks—70
[N.B.
—The figures in the right margin indicate
full marks. Different parts of each question must be answered sequentially.]
Part
A—Short
Questions
(Answer
any five questions)
Marks—6×5=30
1. Define sample and sampling. Briefly discuss
the advantages and
Disadvantages of sampling over population
coverage.
2. Define
with examples: —
(i) Population & sample;
(ii)
Dependent & independent event.
3. Define
sampling and non-sampling errors. What are their sources? How
These
errors can be controlled?
4.
(a) What is Bernoulli trial? Write down
the distribution in which mean
And variance will be same.
(b) What
is the relation among binominal, poison and normal distribution?
5.
(a)
What is student’s distribution?
Under what circumstances t-test is
Applicable.
(b) Write down the properties of
discrete probability function with proof
6.
What
is standard normal variety? Write down the characteristics
of standard normal variety.
7.
SH
company estimates the net profit. On a new product it is launching to be
Tk. 30,00,000 during the first year if it
is successful, Tk. 10,00,000 if it
is moderately successful, and a loss of
Tk. 10,00,000 if it is unsuccessful.
the expected value and standard
deviation of first year net profit for the product is moderately successful,
and a loss of Tk. 10,00,000 if it is unsuccessful. The firm assigns the
following probabilities to first year prospects for the product. Successful :
0.15, moderately successful : 0.25 and unsuccessful : 0.60. What are?
Part—B Broad Questions
(Answer
any five questions)
Marks—10×4=40
8. (a) Write down the importance of normal distribution.
(b) Ten
percent of new automobiles require warranty service within the first
Year Hero Honda Sells 12 automobiles
in January. What is the probability that—
(i)
None of these
automobiles requires warranty service?
(ii)
Exactly two automobiles
require warranty service.
(iii)
Compute the mean and
standard deviation of this probability distribution.
9.
(a)
A workshop produces 2000 units per day. The average weight of units is
13kg with a standard deviation of 10kg.
How many units are expected to weight less than 142kg?
(b)
Recent crime reports indicate that 3.1
motor vehicle thefts occur each minute
in
the Dhaka City. Assume that the distribution of thefts per minute can be
approximated by the poison distribution. What is the probability that—
(i)
Exactly four thefts
occur in a minute.
(ii)
There is at least one
theft in a minute.
10.
(a) Write down the importance of
sampling distribution.
(b)
The estimate of the population proportion is to be within plus or minus
0.05,
with a 95% level of confidence. The best estimate of the population proportion
is 0.15. How large a sample is required?
(c)
A manufacturer of watches has determined
from experience that 3%
of the watches he produces are
defective. If a random sample of 300 watches is examined. What is the
probability that the proportion defective is between 0.02 and 0.35?
11. (a) Define simple probability and
conditional probability.
(b) A
market survey conduct in four cities pertained to preference for brand
A soap. The responses are shown
below :
|
Brand-A
|
Dhaka
|
Rajshahi
|
Chittagong
|
Khulna
|
Total
|
|
45
|
55
|
60
|
50
|
210
|
|
|
Not
Brand-A
|
35
|
45
|
35
|
45
|
160
|
|
No
opinion
|
5
|
5
|
5
|
5
|
20
|
|
Total
|
85
|
105
|
100
|
100
|
390
|
(i)
What is the probability
that a consumer selected at random preferred brand A?
(ii)
What is the probability
that a consumer preferred brand A and was from Chittagong?
(iii)
What is the probability
that a consumer preferred brand A given that he was from Chittagong?
(iv)
Given that a consumer
preferred brand A. What is the probability that was he from Khulna?
12.
(a) What are the main characteristics
of normal distribution?
(b) As
a result of tests on 20,000 electric fans manufactured by a company,
it
was found that lifetime of the fans was normally distributed with an average
life of 2040 hours and standard deviation of 60 hours. On the basis of the
information, estimate the number of fans that is expected to run for (a) more than 2150 hours and (b) less than 1960 hours.
13.
(a) Two sources of raw materials are
under consideration by a company.
Both
sources seem to have similar characteristics but the company is not sure about
their respective uniformity. A sample of 10 lots from source A yields a
variance of 225 and a sample of 11 lots from source B yields a variance of 200.
Is it likely that the variance of source A is significantly greater than the
variance of source B at α = 0.01?
(b) Ten
persons were appointed in an officer cadre in an office. Their performance was noted by giving a
test and the marks were recorded out of 100. They were given 4 months training
and a test held and marks were recorded out 100.
|
Employee
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
|
Before training
|
80
|
76
|
92
|
60
|
70
|
56
|
74
|
56
|
70
|
56
|
|
After training
|
84
|
70
|
96
|
80
|
70
|
52
|
84
|
72
|
72
|
50
|
By
applying the t-test, can it be
concluded that the employees have benefited by the training?
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