Question at position 6 Leah is the operations manager at a chair company. She is getting concerned about the number of wrong customer account numbers recorded. She decides to take measures into her own hands. She conducts a random sample every week of 268 deposits and records the number of incorrect account numbers for 8 weeks. The results for the 8 weeks are listed below. She needs your help to do the first step in her research. Please calculate the p for every week and come up with the average p for the 8 weeks. (Please round your answer to 3 decimal places) [table]
Week | Number defective | Calculate P
1 | 10 | 2 | 12 | 3 | 5 | 4 | 8 | 5 | 22 | 6 | 11 | 7 | 9 | 8 | 7 |
[/table] Answer Leah is the operations manager at a chair company. She is getting concerned about the number of wrong customer account numbers recorded. She decides to take measures into her own hands. She conducts a random sample every week of 268 deposits and records the number of incorrect account numbers for 8 weeks. The results for the 8 weeks are listed below. She needs your help to do the first step in her research. Please calculate the p for every week and come up with the average p for the 8 weeks. (Please round your answer to 3 decimal places) [table]
Week | Number defective | Calculate P
1 | 10 | 2 | 12 | 3 | 5 | 4 | 8 | 5 | 22 | 6 | 11 | 7 | 9 | 8 | 7 |
[/table] [input]

Question

Question at position 6  Leah is the operations manager at a chair company. She is getting concerned about the number of wrong customer account numbers recorded. She decides to take measures into her own hands. She conducts a random sample every week of 268 deposits and records the number of incorrect account numbers for 8 weeks. The results for the 8 weeks are listed below. She needs your help to do the first step in her research. Please calculate the p for every week and come up with the average p for the 8 weeks. (Please round your answer to 3 decimal places) [table]
Week | Number defective | Calculate P
1 | 10 |  2 | 12 |  3 | 5 | 4 | 8 | 5 | 22 |  6 | 11 |  7 | 9 | 8 | 7 |
[/table] Answer Leah is the operations manager at a chair company. She is getting concerned about the number of wrong customer account numbers recorded. She decides to take measures into her own hands. She conducts a random sample every week of 268 deposits and records the number of incorrect account numbers for 8 weeks. The results for the 8 weeks are listed below. She needs your help to do the first step in her research. Please calculate the p for every week and come up with the average p for the 8 weeks. (Please round your answer to 3 decimal places) [table]
Week | Number defective | Calculate P
1 | 10 |  2 | 12 |  3 | 5 | 4 | 8 | 5 | 22 |  6 | 11 |  7 | 9 | 8 | 7 |
[/table] [input]

BlackTom AI · Accepted Answer

We start by interpreting p as the proportion defective in each weekly sample, which is calculated as p = (number defective) / (total deposits). Since each week has 268 deposits, we compute p for each week as follows:

- Week 1: 10 defective -> p = 10 / 268 ≈ 0.0373, rounded to 0.037
- Week 2: 12 defective -> p = 12 / 268 ≈ 0.0448, rounded to 0.045
- Week 3: 5 defective  -> p = 5 / 268 ≈ 0.0187, rounded to 0.019
- Week 4: 8 defective  -> p = 8 / 268 ≈ 0.0299, rounded to 0.030
- Week 5: 22 defective -> p = 22 / 268 ≈ 0.0821, rounded to 0.082
- Week 6: 11 defective -> p = 11 / 268 ≈ 0.0410, rounded to 0.041
- Week 7: 9 defective  -> p = 9 / 268 ≈ 0.0336, rounded to 0.034
- Week 8: 7 defective  -> p = 7 / 268 ≈ 0.0261, rounded to 0.026

Next, we find the average of these eight p-values. Add them together and divide by 8:
0.037 + 0.045 + 0.019 + 0.030 + 0.082 + 0.041 + 0.034 + 0.026 = 0.314
Average p = 0.314 / 8 = 0.03925, which rounds to 0.039 when expressed to three decimals.

Thus, the per-week p-values (rounded to three decimals) are [0.037, 0.045, 0.019, 0.030, 0.082, 0.041, 0.034, 0.026], and the average p across the eight weeks is 0.039 (to three decimals).

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