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ASSIGNMENT
Course Code : MS - 08
Course Title : Quantitative
Analysis for Managerial Applications
Assignment Code : MS-08/SEM - II /2013
Coverage : All Blocks
Q.1
“Statistical unit is necessary not only for the collection of data, but also
for the interpretation and presentation”. Explain the statement.
Answer : Statistics may be defined as
the science of collection, presentation analysis and interpretation of
numerical data from the logical analysis.
The word ‘statistic’ is used to refer to - Numerical
facts, such as the number of people living in particular area. - The study of
ways of collecting, analyzing and interpreting the facts. Statistics is the
study of the collection, organization, analysis, interpretation and
presentation of data. It deals with all aspects of data, including the planning
of data collection in terms of the design of surveys and experiments.
The word statistics, when referring to
the scientific discipline, is singular, as in "Statistics is an art."
This should not be confused with the word statistic, referring to a quantity
(such as mean or median) calculated from a set of data, whose plural is
Q.2 Find the standard deviation and
coefficient of skewness for the following distribution
|
Variable
|
0-5
|
5-10
|
10-15
|
15-20
|
20-25
|
25-30
|
30-35
|
35-40
|
|
Frequency
|
2
|
5
|
7
|
13
|
21
|
16
|
8
|
3
|
Answer : 
Q.3
A salesman has a 60% chance of making a sale to any one customer. The behaviour
of successive customers is independent. If two customers A and B enter, what is
the probability that the salesman will make a sale to A or B.
Answer : The probability that the
salesman fails to make sales to A
The salesman fails to make a sale to B
Q.4
To verify whether a course in Research Methodology improved performance, a
similar test was given to 12 participants before and after the course. The
original marks and after the course marks are given below:
|
Original Marks
|
44
|
40
|
61
|
52
|
32
|
44
|
70
|
41
|
67
|
72
|
53
|
72
|
|
Marks after the course
|
53
|
38
|
69
|
57
|
46
|
39
|
73
|
48
|
73
|
74
|
60
|
78
|
Was
the course useful? Consider these 12 participants as a sample from a
population.
Answer : Let us take the hypothesis
that there is no difference in the marks obtained before and after the course,
i.e. the course has not been useful Applying t-test (difference formula):
Q.5
Write short notes on
a)Bernoulli
Trials
Answer : In the theory of probability
and statistics, a Bernoulli trial is an experiment whose outcome is random and
can be either of two possible outcomes,
"success" and "failure".
Repeated independent trials in which
there can be only two outcomes are called Bernoulli trials in honor of James Bernoulli
(1654-1705).
·
Bernoulli trials lead to the binomial
distribution.
·
If a number of trials are large, then the
probability of k successes in n trials can be approximated by the Poisson distribution.
·
The binomial distribution and t
b)Standard
Normal distribution
Answer : The standard normal
distribution is a special case of the normal distribution . It is the
distribution that occurs when a normal random variable has a mean of zero and a
standard deviation of one.
The normal random variable of a
standard normal distribution is called a standard score or a z score.
Every normal random variable X can be
transformed into a z score via the following equation:
z
= (X - μ) / σ
Where X is a normal random variable, μ
is the mean, and σ is the standard deviation.
c)Central
Limit theorem
Answer : In probability theory, the central limit theorem (CLT) states
that, given certain conditions, the mean of a sufficiently large number of
iterates of independent random variables, each with a well-defined mean and
welldefined variance, will be approximately normally distributed.[1] That is, suppose
that a sample is obtained containing a large number of observations, each
observation being randomly generated in a way that does not depend on the
values of the other observations, and that the arithmetic average of the
observed values is computed. If this procedure is performed many times, the
computed average will not always be the same each time; the central limit
theorem says that the computed values of the
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