Question: A manager wants to investigate a bottling process by using a sample mean chart. He knows from his experience that the process standard deviation is

A manager wants to investigate a bottling process by using a sample mean chart. He knows from his experience that the process standard deviation is 4 mL (milliliter). Each day last week, he randomly selected 9 bottles and measured each. The data (in mL) from that activity appear below.

Weight

Day

Bottle 1

Bottle 2

Bottle 3

Bottle 4

Bottle 5

Bottle 6

Bottle 7

Bottle 8

Bottle 9

Monday

322

325

349

324

323

322

323

324

322

Tuesday

323

321

319

321

323

321

319

321

323

Wednesday

320

319

320

321

320

319

323

321

324

Thursday

318

319

320

319

318

319

320

319

328

Friday

318

320

322

320

318

327

322

320

320
  1. Calculate all the sample means and the mean of all the sample means.

  1. Calculate upper and lower x-bar chart control limits that allow for natural variations with a z value of 3.
  1. Based on the x-bar chart, is this process in control? Create a X-bar chart.
  2. Use the data to (a) create Range chart (b) Based on the R chart, is this process in control?

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