LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Com.,B.B.A. DEGREE EXAMINATION – CORPORATE & BUS.ADMIN.
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FOURTH SEMESTER – APRIL 2008
ST 4208 / 4203 – STATISTICS FOR MANAGEMENT
Date : 24/04/2008 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
- Define a random experiment and give an example.
- A random experiment has the following probability function as follows, find E(X).
| X | -1 | 0 | 1 |
| P(X) | 0.2 | 0.3 | 0.5 |
- Differentiate between statistics and parameters.
- What are the assumptions of analysis of variance test?
- Define index numbers.
- Name any 2 methods of constructing unweighted index numbers.
- What are variable control charts? Name them.
- For a quality control process, the mean is 0.5230 cm and standard deviation is 0.0032 cm. Calculate 3σ upper and lower control limits, if the sample size is 4.
- Define a Linear Programming Problem.
B
- Solve the following game: A
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
- Aakash can solve 3 problems out of 5, Deepak can solve 2 out of 5 and Godfrey can solve 3 out of 4.What is the probability that:
- The problem will be solved
- Only two will solve the problem
- The probability of an increase in demand of a particular product in the next year is 0.75. If this demand increase takes place, the probability that the sales will increase is 0.7. If there is no demand increase, the probability that the sales will increase is 0.5. Given that at the end of the year, the sale has risen, what is the probability that there was an increase in demand of the product?
- A college conducts both day and evening classes intended to be identical. For a sample of 100 day students, the results was: = 72.4 and σ = 14.8 and for a sample of 200 evening students, the exam results was: = 73.9 and σ = 17.9. Are the two means statistically equal at 5% level of significance?
- Edible oil is packed in tins holding 16 Kg each. The filling machine can maintain this but with a standard deviation of 0.5 Kg. Samples of 25 are taken from the production line. If the sample mean is 16.35 Kg, can we be 95 % sure that the sample has come from a population of 16 Kg tins?
- Explain the uses of index numbers, and state the problems in the construction of index numbers.
- The following table gives an inspection data on completed CD’s there were 2000 CD’s in 20 lots of 100 each. Draw a control chart for fraction defectives, and check if the process is in control.
| Lot No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of defectives | 5 | 10 | 12 | 8 | 6 | 5 | 6 | 3 | 3 | 5 |
| Lot No. | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| No. of defectives | 4 | 7 | 8 | 2 | 3 | 4 | 5 | 8 | 6 | 10 |
- Solve the following Linear Programming Problem: Min z = 2 x + y subject to the constraints, x ≤ 4, x + y ≥ 1, 5 x + 10 y ≤ 50, x, y ≥ 0.
- Given the following data, determine the least cost allocation of the available machines M1, M2, M3, M4 and M5, to 5 jobs A, B, C, D and E.
| A | B | C | D | E | |
| M1 | 25 | 29 | 31 | 42 | 37 |
| M2 | 22 | 19 | 35 | 18 | 26 |
| M3 | 39 | 38 | 26 | 20 | 33 |
| M4 | 34 | 27 | 28 | 40 | 32 |
| M5 | 24 | 42 | 36 | 23 | 45 |
SECTION C
Answer any TWO questions. (2 x 20 =40 marks)
- (i) The screws produced by a certain machine were checked by examining samples of 128. The following table shows the distribution of 128 samples according to the number of defective items they contained:
| No. of defectives | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| No. of samples | 7 | 6 | 19 | 35 | 30 | 23 | 7 | 1 |
Fit a binomial distribution and find the expected frequencies if the chance of a screw being defective is ½. Also find the mean and variance of the distribution.
(ii) East-West airlines have the policy of employing women whose height is between 62 and 69 inches. If the height of women is approximately normally distributed with a mean of 64 inches and a standard deviation of 3 inches, out of the 1000 applications receives, find the number of applicants that would be (i) too tall (> 69), (ii) too short (< 62)
- (i) A random sample is selected from each of 3 makes of ropes and their breaking strengths(in pounds) are measured with the following results:
| I | 70 | 72 | 75 | 80 | 83 | ||
| II | 100 | 110 | 108 | 112 | 113 | 120 | 107 |
| III | 60 | 65 | 57 | 84 | 87 | 73 |
Test whether the breaking strength of ropes differ significantly at 5% level of significance.
(ii) Construct Laspeyre’s, Paasche’s and Fisher’s Index numbers for the following data.
| 2006 | 2007 | |||
| Commodity | Price | Quantity | Price | Quantity |
| A | 2 | 8 | 4 | 6 |
| B | 5 | 10 | 6 | 5 |
| C | 4 | 14 | 5 | 10 |
| D | 2 | 19 | 2 | 13 |
- Construct a control chart for mean and range for the following data on the basis of fuses, samples of 5 being taken every hour. Comment on whether the production seems to be under control.
| Sample Number | |||||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 42 | 42 | 19 | 36 | 42 | 51 | 60 | 18 | 69 | 64 | 61 | 15 |
| 65 | 45 | 24 | 54 | 51 | 74 | 60 | 20 | 109 | 90 | 78 | 30 |
| 75 | 68 | 80 | 69 | 57 | 75 | 72 | 27 | 113 | 93 | 94 | 39 |
| 78 | 72 | 81 | 77 | 59 | 78 | 95 | 42 | 118 | 109 | 109 | 620 |
| 87 | 90 | 81 | 84 | 78 | 132 | 138 | 60 | 153 | 112 | 136 | 84 |
- 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 | 3 | 7 | 6 | 4 | 5 |
| B | 2 | 4 | 3 | 2 | 2 |
| C | 4 | 3 | 8 | 5 | 3 |
| Demand | 3 | 3 | 2 | 2 |
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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