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:

Smell

The sense by which odors are perceived, involving the detection of chemical stimuli by the olfactory system.

Peripheral Nervous System

The segment of the nervous system composed of the nerves and ganglia that are located externally to the brain and spinal cord.

Central Nervous System

consists of the brain and spinal cord, serving as the primary processing center for the entire nervous system and coordinating all bodily functions.

Coordination

The ability to use different parts of the body together smoothly and efficiently.