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ASSIGNMENT
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Course Code :
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MS - 8
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Course Title
:
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Quantitative
Analysis for Managerial Applications
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Assignment
Code :
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MS-8/SEM - II
/2014
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Coverage :
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All Blocks
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Note : Attempt all the questions and submit this assignment on or before
30th April, 2016 to the
coordinator of your study centre.
Q1. Explain
the concept of Maxima & Minima and discuss its managerial
applications.
Answer : Maxima and Minima
If the
value of a continious function increases upto a certain point then begins to
decrease, then this point is called point of maximum and corresponding value at
that point is called maximum value of the function. A stage comes when it again
changes from decreasing to increasing . If the value of a continuous function
decreases to a certain point and then begins to increase, then value at that
point is called minimum value of the function and the point is called point of
minimum.
Fig. shows
that a function may have more than one maximum or minimum values. So,
forcontinuous function we have maximum (minimum) value in an interval and these
values are notabsolute maximum (minimum) of the function. For this reason, we
sometimes call them as local maxima or local minima.
Q2. The
average sales of a product for a particular week, excluding Sunday, were
reported by the city departmental store as 150 units. Sunday being
a national festival, there was heavy rush of sales which inflated average sales
for the entire week to 210 units. Find the sales for Sunday.
Answer:
Average sales of a Product for a week (except Sunday) = 150 Units
Total Number of Days (Except Sunday) = 6
Let “ X ” is total sale of
Q3. A
box contains 2 red, 3 black, and 5 white balls. If 3 balls are drawn at random
without replacement, find the probabilities that a) all 3 are black, b) two are
red and one black, c) at least one is white.
Answer.
a) All 3 are black
Probability = number of selection of 3 out of 3 Black balls/Number
of selection of 3 out of 10 balls
Q4. A
firm is manufacturing two brands, A and B, of
battery cells. It claims that the average life of brand A cells
is more than that of brand B cells by 100 hrs, the variances of the two brands
being the same. To maintain this standard, two independent samples of 12 cells
of each brand are selected on the 20th of every month and a t value
of the difference of sample means computed. The firm is satisfied with its
claim if the computed t value falls between ±t0.025. A sample
of 12 cells of brand A gives a mean life of 1200 hrs and
variance of 49 hrs, and that of 12 cells of brand B gives a
mean life of 1095 hrs and variance of 64 hrs. Comment on the outcome of the
sample results.
Answer : The
first step is to state the null hypothesis and an alternative hypothesis.
H0:
μA – μB = 100
Hrs;
H1 : μA – μB ≠
100.
The
significance level is 0.025. Using sample data, we will conduct a two-sample t-test of the null
hypothesis.
Q5. Discuss
the stochastic models developed by Box and Jenkins for time series analysis.
Answer: Box
- Jenkins Analysis refers to a systematic method of identifying, fitting,
checking, and using integrated autoregressive, moving average (ARIMA) time
series models.
The
Box-Jenkins approach is one of the most widely used methodologies for the
analysis of time-series data.It is popular because of its generality; it can
handle any series, stationary or not, with or without seasonal elements, and it
has well-documented computer programs. This methods can we use to forecast
univariate data.
Assumption
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