A graphite manufacturer makes long rolls of flexible graphite to be used to seal components in combustion engines. The specifications state that the mean strength should be 21.2 ounces per square yard with a standard deviation of 0.29. Further specifications state that no roll should have strength less than 20.2 or more than 22.2 ounces per square yard. If there is a defect in terms of the strength of the graphite rolls, the seal will not hold. After the roll is created, a beta scanner takes readings of the basis weight in ounces per square yard. The data is separated into 3 lanes with 20 scans in each lane. A sample consists of one roll from each lane. The results from 20 samples follow:

a)€‚Using the given mean and standard deviation, create an X-bar chart for these samples.
b)€‚Using the given mean and standard deviation, create an R chart for these samples.
c)€‚Is the company€™s process for making flexible graphite sheets out of control?
d)€‚Do all the rolls meet the specification limits?

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Sample Lane1 Lane 2 Lane 3 20.76 21.53 21.69 215321.14 21.06 20.38 20.62 5 21.18 21.29 20.95 21.37 20.65 21.01 21.27 2153 2153 21.14 21.01 2 20.89 21.73 2139 21.55 213421.17 21.72 721.84 21.26 21.05 20.7020.87 22.23 21.27 21.71 21.89 21.24 20.87 20.63 10 20.77 21.24 12 13 14 2209 21.62 15 21.60 21.03 20.68 16 17 18 19 20 21.37 21.29 21.13 21.19 21.56 21.6421.67 21.12 20.88 21.80 21.36 20.56 20.57 20.57 20.37 Sample Lane 1 Lane2 Lane 3 Lane 4 Lane5 Lane 6 Lane 7 Lane 8 Lane 9 Lane 10 121.56 21.59 21.26 21.1621.0121.10 21.22 20.95 20.78 20.66 2 21.42 21.5421.43 21.44 20.99 21.10 20.78 21.17 21.21 21.10 3 21.48 21.2321.19 21.34 21.63 21.47 21.18 2105 21.21 21.22 421.14 21.26 15721.34 21.36 2137 21.42 21.4821.14 21.02 5 21.53 21.26 2143 2126 20.95 20.86 20.99 20.90 20.69 20.80 6 21.40 21.26 21.9 21.38 21.57 2130 20.97 20.72 20.78 20.70 721.84 2151 21.7 21.34 21.38 2132 21.32 21.05 20.57 20.27 8 21.83 21.83 21.56 21.17 20.7420.83 21.00 2135 21.54 2141 9 21.60 215721.44 20.99 20.60 20.83 20.85 20.90 21.14 21.36 10 21.84 21.93 21.9921.97 21.57 21.56 21.17 20.89 21.20 21.28 11 21.96 2150 21.48 21.37 2157 21.68 21.82 21.65 21.20 21.19 12 21.27 253 21.31 21.22 2133 21.31 21.46 21.68 21.69 21.52 1322.03 21.90 22.02 21.46 2134 21.35 21.44 21.84 21.55 21.63 14 21.30 2136 128 21.29 21.00 20.82 20.55 20.48 20.46 20.68 15 21.65 21.18 20.77 20.98 20.92 20.99 21.27 21.56 21.72 21.67 16 21.46 21.52 21.47 21.45 21.3 21.7621.92 21.34 21.11 21.19 17 21.72 21.69 21.77 21.44 21.13 21.1220.9 20.60 20.69 21.07 18 21.67 22.02 21.78 2134 21.00 20.80 20.30 20.54 20.59 21.16 19 21.44 21.28 21.15 20.9720.85 21.17 21.87 21.6721.5921.20 20 238 21.32 20.91 21.10 21.17 21.58 21.53 21.54 21.1220.69 21 2123 2130 21.57 21.42 21.52 21.42 20.90 20.85 20.60 20.71 22 21.65 21.33 21.44 21.27 21.06 20.80 20.82 20.84 20.9821.22 23 21.59 21.58 21.13 2134 21.57 2147 21.55 21.83 21.56 21.02 24 20.92 20.74 20.30 20.07 20.48 20.39 20.81 20.90 21.18 21.18 25 21.02 21.03 21.00 21.04 21.15 21.10 21.24 21.09 21.25 20.86