T. Crews, Inc. has been contracted to make Foolio. The recipe calls for 100 mill
ID: 2747465 • Letter: T
Question
T. Crews, Inc. has been contracted to make Foolio. The recipe calls for 100 milligrams of taurine in each 16 ounce bottle. To make sure that they are in compliance, T. Crews has pulled eight bottles of Foolio from its last eleven batches and tested them for taurine content. The data from these tests is below.
1. What is UCLR?
Less than 18.25
Between 18.26 and 18.75
Between 18.76 and 19.25
Greater than 19.26
2. What is LCLR?
Less than 1.00
Between 1.01 and 1.25
Between 1.26 and 1.50
More than 1.51
3. All points on the R-chart are within the control limits.
True
False
4. What is UCLX-bar?
Less than 110.00
Between 110.10 and 112.00
Between 112.01 and 114.00
Between 114.01 and 116.00
Greater than 116.01
5. What is LCLX-bar?
Less than 96.00
Between 96.01 and 97.00
Between 97.01 and 98.00
Between 98.01 and 99.00
Greater than 99.01
6. All points on the X-bar chart are within the control limits.
True
False
7. Is this process considered in control?
Yes, because all points on the r-chart are within the control limits
Yes, because all points on the r-chart and x-bar chart are within the control limits
No, because points on the r-chart or x-bar chart are not within the control limits
No, because points on R chart are too close to average
A.Less than 18.25
B.Between 18.26 and 18.75
C.Between 18.76 and 19.25
D.Greater than 19.26
Mg taurine per bottle Batch Bottle l Bottle 2 Bottle 3 Bottle 4 Bottle 5 Bottle 6 Bottle7 Bottle 8 104.87105.65 106.52 107.40 106.95 108.65 110.52 111.00 97.65 100.33 94.80 04.80101.61 103.46 103.90 101.87 101.72 108.00 102.70 97.43 102.85 106.12 109.62 104.60 101.19105.33 98.66 105.61 99.55100.08 98.85 101.75 102.89 02.05 102.84 10.57 98.58101.25 108.85 105.98 108.50 105.06 102.89 99.15 105.15104.12 99.76 102.17 102.47 104.92 103.48 100.86 113.58 104.68 102.25 105.86 98.95 100.62 105.45 105.21 99.37 102.50100.92 98.22 100.00 96.63 97.6 102.50 101.23 109.81 105.25 111.20101.85 109.50 98.15100.46 94.11 108.78 108.65 99.80 99.75 106.83 9 10 108.52105.57 107.50 103.39 104.01104.56 103.98Explanation / Answer
Range for each batch is calculated (maximum - minimum) as follows:
Average Range = 10.21182 (112.33/11)
UCL for Rchart is D4 * Average Range = 1.864* 10.21182 = 19.03483
LCT for Rchart is D3 * Average Range = .136 * 10.21182 = 1.388807
1. What is UCLR?
Between 18.76 and 19.25
2. What is LCLR?
Between 1.26 and 1.50
3. All points on the R-chart are within the control limits.
True
Value of A2 in the present case is .373, Grand Mean (mean of the sample means) = 103.582, therefore
UCL = 107.3911 and LCL = 99.77304
4. What is UCLX-bar?
Less than 110.00
5. What is LCLX-bar?
Greater than 99.01
6. All points on the X-bar chart are within the control limits.
Batch 2 has mean less than LCL
False
7. Is this process considered in control?
Yes, because all points on the r-chart are within the control limits
No, because points on the r-chart or x-bar chart are not within the control limits
Batch 1 2 3 4 5 6 7 8 9 10 11 Range 6.13 6.12 6.39 13.8 11 11.72 14.7 9.35 12.72 9.7 9.15Related Questions
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