Construct An $\bar { x }$ Chart
Control Chart Constants A Machine Is Supposed to Fill Boxes to a Weight

question 89

Essay

Construct an $\bar { x }$ chart.
Control Chart Constants
$\begin{array}{ccccccc}&\bar{x}&&s&&R\\\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.
$\begin{array} { c | c c c c | c | c } \text { Sample } &&& { \text { Beight (lb) } } && \overline { \boldsymbol { x } } & \text { Range } \\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 61 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50.00 & 28 \\4 & 44 & 59 & 46 & 49 & 49.50 & 15 \\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 48 & 47.25 & 5 \\7 & 52 & 51 & 45 & 55 & 50.75 & 10 \\8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\9 & 48 & 67 & 60 & 51 & 56.50 & 19 \\10 & 43 & 50 & 50 & 47 & 47.50 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18 \\12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\13 & 50 & 58 & 56 & 64 & 57.00 & 14 \\14 & 47 & 52 & 47 & 49 & 48.75 & 5 \\15 & 52 & 57 & 58 & 52 & 54.75 & 6\end{array}$

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Definitions:

Normal Balance

The normal balance is the side (debit or credit) of an account that is expected to have a higher balance based on the accounting equation.

Financial Statement(s)

Reports summarizing the financial performance, position, and cash flows of a business over a specified period, including balance sheet, income statement, and cash flow statement.

Permanent/Temporary

Defines classifications of accounts in accounting where permanent accounts refer to balance sheet items that carry over into the next fiscal period, while temporary accounts are closed at the end of each accounting period.

Normal Balance

The side (debit or credit) of an account that is expected to have a higher balance, indicating the account’s increase.