Construct a 3-Sigma $\overline { X }$ - and R-Chart for the Length in Centimeters of a for the Length

question 224

Essay

Construct a 3-sigma $\overline { X }$
- and R-chart for the length in centimeters of a part from the following table.
$\begin{array}{c}\quad\quad\quad\text { Observation }\\\begin{array}{crrrrr}\text { Sample \# } & 1 & 2 & 3 & 4 \\\hline 1 & 0.486 & 0.499 & 0.493 & 0.511 \\2 & 0.499 & 0.506 & 0.516 & 0.494 \\3 & 0.496 & 0.5 & 0.515 & 0.488 \\4 & 0.495 & 0.506 & 0.483 & 0.487 \\5 & 0.472 & 0.502 & 0.526 & 0.469 \\6 & 0.473 & 0.495 & 0.507 & 0.493 \\7 & 0.495 & 0.512 & 0.49 & 0.471 \\8 & 0.525 & 0.501 & 0.498 & 0.474 \\9 & 0.497 & 0.501 & 0.517 & 0.506 \\10 & 0.495 & 0.505 & 0.516 & 0.511\end{array}\end{array}$

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Definitions:

Expected Returns

The predicted amount of profit or loss an investment is projected to generate, often based on historical data or statistical models.

Standard Deviation

A statistical measure of the dispersion or variability in a set of data points, often used to gauge the risk associated with a financial asset.

Good Economy

A state of economic health in which a nation experiences growth, low unemployment, and increasing wealth among its population.

Poor Economy

A state of economic performance characterized by low growth rates, high unemployment, and generally declining business activity.