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ASSIGNMENT
Course Code : MS – 8
Course Title : Quantitative Analysis for Managerial Applications
Assignment Code : MS-8/ TMA /SEM – II /2015
Coverage : All Blocks
Note: Attempt all the questions and submit this assignment on or before 31st October, 2015 to the coordinator of your study centre.
Q.1. The frequency distribution of total annual emoluments of a sample of 100 executives working in multinational companies is given below:
| Total Emoluments
(in Rs Lac) |
02–06 | 06 –10 | 10-14 | 14 -18 | 18-22 | 22-26 | 26-30 |
| Number of Executives | 10 | 15 | 30 | 18 | 12 | 09 | 06 |
Find a) median emoluments, b) mode emoluments, c) 3rd quartile, and d) 9th decile.
Answer:Some textbooks and professors do it slighly different. I think this isn’t much different, if any, from what you are being taught.The frequency polygon is just a bunch of lines connecting the middle of the tops of the histogram bars, so it’s this green zig-
- 2. A population consisting of a certain proportion of defective items has mean μ = 2. If a sample of 4 items is examined and repeated 200 times, obtain a) probability of an item being defective, b) probability of getting 2 defective items in the sample, c) expected frequency of getting 2 defective items, and d) expected frequency of getting at the most 2 defective items. Is the resultant distribution skewed?
Answer:Suppose A and B are two events in a given situation. If A and B cannot possibly occur simultaneously they are said to be mutually exclusive events.For mutually exclusive events the probability that one event or the other occurs is given by:
- 3. A research organization claims that the monthly wages of industrial workers in district X exceeds that of those in district Y by more than Rs 150. Two different samples drawn independently from the two districts yielded the following results:
District X:
District Y:
Verify at 0.05 level of significance whether the sample results support the claim of the organization.
Answer:The procedure is explained in the following steps:
test statistics=(x1 bar- x2 bar)(s1^2/n1)(s2^2/n2)
substitute the values and you will get the answer.
I got this answer. please check it.
(x1 bar- x2 bar)(s1^2/n1)(s2^2/n2)
⇒(648-495)(120/100)(140/90)
- 4. The following data relate to marketing expenditure in Rs lac and the corresponding sales of a product in Rs crores. Estimate the marketing expenditure to attain a sales target of Rs 40 crores.
| Marketing expenditure | 10 | 12 | 15 | 20 | 23 |
| Product sales | 14 | 17 | 23 | 21 | 25 |
Answer:A company has the capacity to produce goods worth of Rs. 40 crores a year. For this has incurred a fixed cost of Rs 20 crores, the variable costs being 60% of the sales revenue. Now company is planning to incur an additional Rs. 6 crores in feed costs to expand its production capacity from Rs. 40 crores to Rs.60 crores. The survey shows that the firm’s sales can be increased from Rs. 40 crores to Rs. 50 crores. Should the firm go in for expansion?
- 5. Write short notes on:
- i) Adjoint of a matrix
Answer:In linear algebra, the adjugate, classical adjoint, or adjunct of a square matrix is the transpose of the cofactor matrix. The adjugate has sometimes been called the “adjoint”, but today the “adjoint” of a matrix normally refers to its corresponding adjoint operator, which is its conjugate transpose.
The adjugate of A is the transpose of the cofactor matrix C of A,
In more detail, suppose R is a comm.
- ii) Skewness and its measures
Answer:In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or even undefined. The qualitative interpretation of the skew is complicated. For a unimodal distribution, negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the
iii) Business forecasting
Answer:BUSINESS FORECASTING is an estimate or prediction of future developments in business such as sales, expenditures, and profits. Given the wide swings in economic activity and the drastic effects these fluctuations can have on profit margins, it is not surprising that business forecasting has emerged as one of the most important aspects of corporate planning. Forecasting has become an invaluable tool for businesspeople to anticipate economic trends and prepare themselves either to benefit from or to counteract them. If
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