Harris Hemp Company tests the tensile strength of a certain manufactured industrial grade rope. The specifications for this product stipulate a minimum tensile strength of 440 kilogram (kg).

a. Construct control charts to determine if the process is in control.
b. Use the data collected to estimate the process average tensile strength and the standard deviation.
c. What percentage of the process output would you estimate is below the minimum required tensile strength?
d. Assuming that the process standard deviation continues at its current level, where should the process be centered so that less than one rope in one million will fail to meet the minimum specification?
e. Assuming that the process average continues at its current level, by what percentage would the process variance have to be reduced so that less than one rope in one million will fail to meet the minimum specification?

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Tensile Strengh (Kg s) Sample 4 2 488 495 467 484 488 471 465 471 474 460 495 452 503 494 461 501 464 483 473 488 492 457 485 483 487 489 485 492 487 464 478 464 482 476 466 497 492 492 486 500 493 451 479 490 497 522 499 478 483 465 466 478 488 488 484 4 6 484 461 484 472 490 498 495 449 480 495 489 477 485 467 481 474 495 498 491 9 10 473 462 491 470 491 12 13 15 16 17 18 19 20 21 474 499 474 479 506 467 465 470 502 500 490 494 492 23 24 25 489 468