Construct a three-sigma x-chart and r chart


Problem:

Sample   Observations      
Number 1 2 3 4 5
1 0.486 0.499 0.493 0.511 0.481
2 0.499 0.506 0.516 0.494 0.529
3 0.496 0.5 0.515 0.488 0.521
4 0.495 0.506 0.483 0.487 0.489
5 0.472 0.502 0.526 0.469 0.481
6 0.473 0.495 0.507 0.493 0.506
7 0.495 0.512 0.49 0.471 0.504
8 0.525 0.501 0.498 0.474 0.485
9 0.497 0.501 0.517 0.506 0.516
10 0.495 0.505 0.516 0.511 0.497
11 0.495 0.482 0.468 0.492 0.492
12 0.483 0.459 0.526 0.506 0.522
13 0.521 0.512 0.493 0.525 0.51
14 0.487 0.521 0.507 0.501 0.5
15 0.493 0.516 0.499 0.511 0.513
16 0.473 0.506 0.479 0.48 0.523
17 0.477 0.485 0.513 0.484 0.496
18 0.515 0.493 0.493 0.485 0.475
19 0.511 0.536 0.486 0.497 0.491
20 0.509 0.49 0.47 0.504 0.512

a. Construct a three-sigma X chart and R chart for the length of the fuel injector. What can you say about this process?

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