Question: 1. SohnCo. Engineered Systems has developed a solution to the problem of problem #1. They have developed a custom torque wrench (the SohnCo. 2025 robo-torque

1. SohnCo. Engineered Systems has developed a solution to the problem of problem #1. They have developed a custom torque wrench (the SohnCo. 2025 robo-torque wrench) for golf cleats that installs the cleat and turns it to the appropriate tightness. The design specification for Jiang Sports America cleats is 10.5 inch-lbs plus or minus 1.2 inch pounds. The CEO of SohnCo. Engineered Systems is a competitor and a bit of a gambler. He offers a gamble to the CEO of Jiang Sports America. He offers a $100,000 prize if Jiang Sports America uses the SohnCo. 2025 correctly and in a test if Cpk is less than 1.5 than he pays the $100,000 to an agreed-on charity. If the SohnCo. 2025 meets the specifications and a C pk of 1.5 or greater, Jiang Sports America buys five of the SohnCo. 2025 machines. Below are some data from the agreed-on test: 25 subgroups of 4 pairs of shoes each.

(These data are also in the Excel file.)

Group X1 X2 X3 X4 1 9.8113 10.3155 9.4486 9.6562 2 9.9807 10.1495 9.5061 10.5058 3 9.8603 10.3058 10.686 10.6404 4 9.3547 9.9601 10.5113 9.9282 5 9.3407 10.2561 10.1955 9.4311 6 10.6556 9.7505 10.5353 9.8918 7 10.6568 10.2188 10.2188 9.9223 8 10.388 10.3088 10.1603 10.1475 9 10.8432 9.9731 9.354 9.8132 10 9.4474 9.288 9.7361 9.5779 11 9.6671 9.8727 9.88 10.0715 12 9.9852 9.6935 10.0482 10.3816 13 10.1086 10.0123 10.0369 9.8546 14 10.3101 9.6873 9.9494 9.576 15 9.5472 9.9525 10.7503 10.1195 16 9.8813 9.6569 9.879 11.1829 17 10.3828 9.8176 9.7485 10.3659 18 10.3027 10.036 9.4744 10.081 19 10.4669 10.5607 9.8373 10.1474 20 9.7649 10.3439 9.5559 10.3405 21 10.1037 10.9678 10.1152 10.1528 22 9.9361 9.9768 10.3254 10.668 23 10.0605 9.9559 9.282 9.631 24 10.2203 9.6116 9.6701 10.4095 25 10.079 10.6764 10.3765 10.8353

Please assess the gamble. Did the SohnCo. 2025 meet the challenge? You must certify the Cpk and other aspects of the bet.

Suppose before the test, they took another action: $500 to charity per too loose spike and $300 per too tight (Torque too high) over the next 1000 pairs of cleats. Determine their total donation.

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