LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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BBA & B.Com. Corp. DEGREE EXAMINATION
FOURTH SEMESTER – APRIL 2007
ST 4203 – STATISTICS FOR MANAGEMENT
Date & Time: 19/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
- Define equally likely events and give an example.
- The mean of a Binomial distribution is 4 and variance is 3. Find P(X = 15).
- What is the objective of statistical quality control?
- Name some variable control charts.
- State the addition theorem of probability.
- What are index numbers? What do they measure?
- State any two methods of constructing weighted index numbers.
- State the minimax-maximin principle in game theory.
- Find the value of the game:
| B1 | B2 | |
| A1 | 0 | 2 |
| A2 | -1 | 4 |
- What are the two types of errors in testing of hypothesis?
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
- An urn contains 6 white, 4 red and 9 blue balls. If 3 balls are drawn at random, find the probability that,
- 2 of the balls drawn are white, (ii) one is of each colour
- none is red, (iv) atleast one is white
- For a Binomial distribution with parameters n = 5, p = 0.3, find the probabilities of getting, (i) atleast 3 successes, (ii) atmost 3 successes
(iii) exactly 3 failures, (iv) exactly 3 successes
- Construct a control chart for C, ie., number of defects from the following data pertaining to the imperfections in 20 pieces of cloth of equal length in a certain make of polyester and infer whether the process is in a state of control: 2, 3, 5, 8, 12, 2, 3, 4, 6, 5, 6, 10, 4, 6, 5, 7, 4, 9, 7, 3.
- Explain quality assurance, statistical process control, and types of control charts.
- The following data relate to the prices and quantities of 5 commodities in the years 2005 and 2006. Construct the following index numbers for prices for the year 2006, taking 2005 as the base, (i) Laspeyre’s, (ii) Paasche’s, (iii) Fisher’s Ideal,
(iv) Bowleys.
| Commodities
|
Base Year | Current Year | ||
| Quantity | Price | Quantity | Price | |
| A | 8 | 4 | 10 | 9 |
| B | 7 | 3 | 8 | 5 |
| C | 6 | 4 | 5 | 8 |
| D | 5 | 2 | 7 | 4 |
- (i) Define Linear Programming.
(ii) A company has 3 operational departments (weaving, processing and packing) with capacity to produce 3 different types of clothes namely suitings, shirtings and woolens yielding profit of Rs. 2, Rs. 4, and Rs. 3 per metre respectively. One metre suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly one metre of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minute in packing, while one metre of woolen requires 3 minutes in each department. In a week, total run time of each department is 60, 40 and 80 hours for weaving, processing and packing departments respectively. Formulate the LPP to find the product mix to maximize the profit.
- Solve the following game graphically:
Player B
Player A
- Set up an ANOVA table for the following per hectare yield (in 100 Kgs) for 3 varieties of rice, each grown in 4 plots:
| Variety of rice | |||
| Plots of land | R1 | R2 | R3 |
| 1 | 6 | 5 | 5 |
| 2 | 7 | 5 | 4 |
| 3 | 3 | 3 | 3 |
| 4 | 8 | 7 | 4 |
Test whether there is significant difference among the average yields in the 3 varieties of wheat, at 5 % level.
SECTION C
Answer any TWO questions. (2 x 20 =40 marks)
- (i) Write down the probability distribution function of a Poisson random variable, and fit a poisson distribution to the following data: (Given e _ .05 = 0.61)
| X | 0 | 1 | 2 | 3 | 4 |
| Frequency | 122 | 122 | 60 | 15 | 2 |
(ii) Students of a class were given an aptitude test. Their marks were found to be normally distributed with mean 60 and standard deviation 5. What percentage of the students scored:
- more than 60 marks, (b) less than 56 marks (c) between 45 and 65 marks. (12 + 8)
- From the following data calculate the control limits for the mean and range control charts and also check if the process is in control. Measurements of the units are given in cms.
| S.No of Samples | |||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 50 | 51 | 50 | 48 | 46 | 55 | 45 | 50 | 47 | 56 |
| 55 | 50 | 53 | 53 | 50 | 51 | 48 | 56 | 53 | 53 |
| 52 | 53 | 48 | 50 | 44 | 56 | 53 | 54 | 49 | 55 |
| 49 | 50 | 52 | 51 | 48 | 47 | 48 | 53 | 52 | 54 |
| 54 | 46 | 47 | 53 | 47 | 51 | 51 | 57 | 54 | 52 |
U
N
I
T
S
| Commodity | 2002 | 2003 | 2004 | 2005 | 2006 |
| I | 2 | 3 | 5 | 7 | 8 |
| II | 8 | 10 | 12 | 4 | 18 |
| III | 4 | 5 | 7 | 9 | 12 |
- (i) Calculate fixed base index numbers and chain base index numbers for the following
(ii) Determine the least cost allocation of the available machines to 5 jobs.
| Jobs | |||||
| Machines | A | B | C | D | E |
| 1 | 25 | 29 | 31 | 42 | 37 |
| 2 | 22 | 19 | 35 | 18 | 26 |
| 3 | 39 | 38 | 26 | 20 | 33 |
| 4 | 34 | 27 | 28 | 40 | 32 |
| 5 | 24 | 42 | 36 | 23 | 45 |
(10 + 10)
- There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.
| D | E | F | G | Supply | |
| A | 6 | 8 | 8 | 5 | 30 |
| B | 5 | 11 | 9 | 7 | 40 |
| C | 8 | 9 | 7 | 13 | 50 |
| Demand | 35 | 28 | 32 | 25 |
Find out the solution for transporting the products at a minimum cost by using (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best solution.
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