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Choose the correct alternative:
The LCL for R chart is given by
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From the following data, calculate the control limits for the mean and range chart.
| Sample No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sample Observations |
50 | 21 | 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 | 549 | 55 | |
| 49 | 50 | 52 | 51 | 48 | 47 | 48 | 53 | 52 | 54 | |
| 54 | 46 | 47 | 53 | 47 | 51 | 51 | 47 | 54 | 52 |
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The following data gives the average life(in hours) and range of 12 samples of 5lamps each. The data are
| Sample No | 1 | 2 | 3 | 4 | 5 | 6 |
| Sample Mean | 1080 | 1390 | 1460 | 1380 | 1230 | 1370 |
| Sample Range | 410 | 670 | 180 | 320 | 690 | 450 |
| Sample No | 7 | 8 | 9 | 10 | 11 | 12 |
| Sample Mean | 1310 | 1630 | 1580 | 1510 | 1270 | 1200 |
| Sample Range | 380 | 350 | 270 | 660 | 440 | 310 |
Construct control charts for mean and range. Comment on the control limits.
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The following are the sample means and I ranges for 10 samples, each of size 5. Calculate; the control limits for the mean chart and range chart and state whether the process is in control or not.
| Sample Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mean | 5.10 | 4.98 | 5.02 | 4.96 | 4.96 | 5.04 | 4.94 | 4.92 | 4.92 | 4.98 |
| Range | 0.3 | 0.4 | 0.2 | 0.4 | 0.1 | 0.1 | 0.8 | 0.5 | 0.3 | 0.5 |
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Given the following pay-off matrix(in rupees) for three strategies and two states of nature.
| Strategy | States-of-names | |
| E1 | E2 | |
| S1 | 40 | 60 |
| S2 | 10 | – 20 |
| S3 | – 40 | 150 |
Select a strategy using the following rule (i) Maximin (ii) Minimax
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A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.
| Rainfall | Estimated Conditional Profit (Rs.) | ||
| Crop A | Crop B | Crop C | |
| High | 8000 | 3500 | 5000 |
| Medium | 4500 | 4500 | 5000 |
| Low | 2000 | 5000 | 4000 |
If the farmer wishes to plant only crop, decide which should be his best crop using (i) Maximin (ii) Minimax
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The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-off s for various level of sales.
| Types of shampoo | Estimated Sales (in Units) | ||
| 15000 | 10000 | 5000 | |
| Egg shampoo | 30 | 10 | 10 |
| Clinic shampoo | 40 | 15 | 5 |
| Deluxe shampoo | 55 | 20 | 3 |
What will be the marketing manager’s decision if (i) Maximin and (ii) Minimax principle applied?
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Following pay-off matrix, which is the optimal decision under of the following rule (i) maximin (ii) minimax
| Act | States of nature | |||
| S1 | S2 | S3 | S4 | |
| A1 | 14 | 9 | 10 | 5 |
| A2 | 11 | 10 | 8 | 7 |
| A3 | 9 | 10 | 10 | 11 |
| A4 | 8 | 10 | 11 | 13 |
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Choose the correct alternative:
Decision theory is concerned with
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Choose the correct alternative:
A type of decision–making environment is
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A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:
| Alternative | Economic conditions | ||
| High growth (Rs.) | Normal growth (Rs.) | Slow growth (Rs.) | |
| Stocks | 10 | 7000 | 3000 |
| Bonds | 8000 | 6000 | 1000 |
| Debentures | 6000 | 6000 | 6000 |
Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax
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