Quarters. In Exercises 9–12, refer to the accompanying table o...

Question

Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B.
Quarters: Notation Find the values of x(doublebar) and Rbar. Also find the values of LCL and UCL for an R chart.

Quarters: Notation Find the values of x(doublebar) and Rbar. Also find the values of LCL and UCL for an R chart.

Accepted Answer

Hello, everyone, let's take a look at this question together. Refer to the accompanying table of notebook batteries recorded at 4 different time intervals on 5 different dates. These values represent the quality control measures used to ensure consistent battery weight. And here we have our data of the notebook batteries recorded at the 4 different time intervals on the 5 different days, and we have to compute the average sample mean and the average range using the data above, as well as find the control limits for the R chart. And the first step in solving this problem is to calculate X bar which X. can be calculated using the following formula, which plugging in the values from the given data, we can calculate X bar as 12.466, which can be rounded to 12.5, and then we calculate R bar, which can be calculated using the formula for R bar and plugging in the values from the given data, we get 0.0. 5. Then the next step is to compute the control limits, which for control charts we use the D3 and the D4 factors which depend on the subgroup size. And since in this scenario N is equal to 4, D3 is equal to 0, and D4 is equal to 2.282. So then the next step is to compute the R chart control limits. Using the lower control limit for R, which can be calculated as D3 multiplied by R bar, which plugging in the values we calculated results in 0 multiplied by 0.05, giving us the value of 0 for the lower control limit, and then for the upper control limit of R, we calculate that by taking the D4 value multiplied by. Bar, which is 2.282, multiplied by 0.05, giving us 0.1141 as the value for the upper control limit. So we have the values for X bar, which is 12.5, our bar, which is 0.05, the lower control limit which is 0, and the upper control limit which is 0.114. And looking at our. Choices, we can identify that the answer choice containing all of the correct values is answer choice C. as X bar is equal to 12.5, our bar is 0.05, the lower control limit is 0, and the upper control limit is 0.114. So answer choice C is the only correct answer choice. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Mean (x̄)

Range (R)

Control Limits (LCL and UCL)

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