Sample Size, n 2 3 4 6 8 9 10 12 Mean Factor, A₂ 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, D4 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 Lower Control Limit (LCL) = b) The control limits for the 3-sigma Upper Control Limit (UCLR) Lower Control Limit (LCLR)= Lower Range, D3 0 0 0 0 0 0.076 0.136 0.184 0.223 0.284 Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 60.75 lb.; Average range R = 1.78 lb. a) For the given sample size, the control limits for 3-sigma x chart are: Upper Control Limit (UCL;)=Ib. (round your response to three decimal places). lb. (round your response to three decimal places). R-chart are: Ib. (round your response to three decimal places). Ib. (round your response to three decimal places).

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### Transcription for Educational Website:

#### Table of Control Chart Factors

| Sample Size, n | Mean Factor, \( A_2 \) | Upper Range, \( D_4 \) | Lower Range, \( D_3 \) |
|----------------|-----------------------|---------------------|---------------------|
| 2              | 1.880                 | 3.268               | 0                   |
| 3              | 1.023                 | 2.574               | 0                   |
| 4              | 0.729                 | 2.282               | 0                   |
| 5              | 0.577                 | 2.115               | 0                   |
| 6              | 0.483                 | 2.004               | 0                   |
| 7              | 0.419                 | 1.924               | 0.076               |
| 8              | 0.373                 | 1.864               | 0.136               |
| 9              | 0.337                 | 1.816               | 0.184               |
| 10             | 0.308                 | 1.777               | 0.223               |
| 12             | 0.266                 | 1.716               | 0.284               |

#### Description of Sample Data:

Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were:
- Overall mean = 60.75 lb.
- Average range \( \overline{R} \) = 1.78 lb.

#### Control Limits Calculations:

**a) For the given sample size, the control limits for the 3-sigma \( \bar{x} \) chart are:**

- Upper Control Limit (UCL\(_{\bar{x}}\)) = \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) lb. (round your response to three decimal places).

- Lower Control Limit (LCL\(_{\bar{x}}\)) = \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) lb. (round your response to three decimal places).

**b) The control limits for the 3-sigma R-chart are:**

- Upper Control Limit (UCL\(_R
Transcribed Image Text:### Transcription for Educational Website: #### Table of Control Chart Factors | Sample Size, n | Mean Factor, \( A_2 \) | Upper Range, \( D_4 \) | Lower Range, \( D_3 \) | |----------------|-----------------------|---------------------|---------------------| | 2 | 1.880 | 3.268 | 0 | | 3 | 1.023 | 2.574 | 0 | | 4 | 0.729 | 2.282 | 0 | | 5 | 0.577 | 2.115 | 0 | | 6 | 0.483 | 2.004 | 0 | | 7 | 0.419 | 1.924 | 0.076 | | 8 | 0.373 | 1.864 | 0.136 | | 9 | 0.337 | 1.816 | 0.184 | | 10 | 0.308 | 1.777 | 0.223 | | 12 | 0.266 | 1.716 | 0.284 | #### Description of Sample Data: Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: - Overall mean = 60.75 lb. - Average range \( \overline{R} \) = 1.78 lb. #### Control Limits Calculations: **a) For the given sample size, the control limits for the 3-sigma \( \bar{x} \) chart are:** - Upper Control Limit (UCL\(_{\bar{x}}\)) = \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) lb. (round your response to three decimal places). - Lower Control Limit (LCL\(_{\bar{x}}\)) = \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_) lb. (round your response to three decimal places). **b) The control limits for the 3-sigma R-chart are:** - Upper Control Limit (UCL\(_R
Expert Solution
Step 1: Determine the given variables

Overall mean (X-double bar) = 60.75 lb

Average range (R-bar) = 1.78 lb

Sample size (n) = 7

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