Thirty successive heats of a steel alloy are tested at the Midwest Steel Works. The resulting data have been recorded in the following table.

a. Use appropriate control charts to determine if the alloy hardness is in a state of statistical control.
b. Use appropriate control charts to determine if the alloy hardness is in a state of statistical control.
c. By what percentage would the process variance need to be reduced to ensure that no more than 0.1% of the heats fail to comply with the minimum hardness requirement?

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Hardness Heat Hea( NumberData) Hardness d Number (Coded 16 56 54 51 57 56 53 59 52 56 57 54. 56 54 52 57 54 19 20 21 58 57 57 57 53 53 56 7 23 24 25 26 27 28 29 30 12 13 14 15 53 58 56