Number Reworked Number Produced Number Number Month Produced Month Reworked 1 23 3 11 17 3 2 28 3 12 4 3 16 1 13 14 4 6 14 41 2 15 18 6 6 32 4 16 7 29 17 33 4 8 19 18 46 9 12 1 19 21 7 10 7 1 20 29 7
Applied Machines produces large test equipment for integrated circuits. The machines are made to order, so the production rate varies from month to month. Before shipping, each machine is subject to extensive testing. Based on the tests the machine is either passed or sent back for rework. During the past 20 months the firm has had to rework the following numbers of machines: (given)
Consider the example of Applied Machines presented above. Based on the estimate of the probability that a machine is sent back for rework computed from the 20 months of data, determine the following:
a. If the company produces 35 machines in one particular month, how many, on average, require rework?
b. Out of 100 machines produced, what is the probability that more than 20 percent of them require rework? (Use the normal approximation to the binomial for your calculations).
| Month | Number produced | Number reworked | Proportion reworked |
| 1 | 23 | 3 | 0.13043478 |
| 2 | 28 | 3 | 0.10714286 |
| 3 | 16 | 1 | 0.0625 |
| 4 | 6 | 0 | 0 |
| 5 | 41 | 2 | 0.04878049 |
| 6 | 32 | 4 | 0.125 |
| 7 | 29 | 5 | 0.17241379 |
| 8 | 19 | 2 | 0.10526316 |
| 9 | 12 | 1 | 0.08333333 |
| 10 | 7 | 1 | 0.14285714 |
| 11 | 17 | 3 | 0.17647059 |
| 12 | 4 | 0 | 0 |
| 13 | 14 | 2 | 0.14285714 |
| 14 | 0 | 0 | 0 |
| 15 | 18 | 6 | 0.33333333 |
| 16 | 0 | 0 | 0 |
| 17 | 33 | 4 | 0.12121212 |
| 18 | 46 | 5 | 0.10869565 |
| 19 | 21 | 7 | 0.33333333 |
| 20 | 29 | 7 | 0.24137931 |
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