The Table Below Shows the Data from Samples of Size $n=5$

question 48

Essay

The table below shows the data from samples of size $n=5$ randomly chosen from the outputs of a process on 20 different days.
$\begin{array}{cccccc}\hline \text { Sample } & & & \text { Data } & & \\\hline 1 & 4.5 & 2.1 & 5.4 & 2.7 & 4.5 \\2 & 3.6 & 3.5 & 6.1 & 4.9 & 4.2 \\3 & 5.1 & 6.2 & 2.4 & 3.7 & 5.1 \\4 & 4.9 & 5.4 & 3.5 & 5.4 & 3.7 \\5 & 4.1 & 3.8 & 3.8 & 4.6 & 4.9 \\6 & 3.7 & 4.6 & 4.8 & 4.2 & 5.2 \\7 & 5.6 & 4.7 & 4.1 & 5.1 & 3.1 \\8 & 4.8 & 5.1 & 4.3 & 4.6 & 2.7 \\9 & 6.1 & 4.6 & 4.7 & 3.8 & 4.2 \\10 & 2.4 & 4.8 & 5.6 & 4.1 & 4.8 \\11 & 3.7 & 5.3 & 2.9 & 4.7 & 6.3 \\12 & 4.5 & 3.4 & 3.4 & 5.2 & 4.5 \\13 & 5.2 & 2.7 & 5.1 & 6.2 & 2.9 \\14 & 3.4 & 5.5 & 4.6 & 2.4 & 3.4 \\15 & 4.8 & 3.6 & 4.8 & 4.4 & 4.6 \\16 & 4.1 & 4.6 & 4.9 & 4.9 & 4.3 \\17 & 4.6 & 3.7 & 3.5 & 3.7 & 5.2 \\18 & 5.1 & 4.2 & 5.6 & 4.1 & 5.7 \\19 & 3.7 & 4.8 & 4.9 & 2.3 & 4.5 \\20 & 5.4 & 3.9 & 4.2 & 5.4 & 4.3 \\\hline\end{array}$

a. $\text { Find } D_{3} \text { and } D_{4} \text {. }$
b. $\text { Construct an R-chart. }$
c. $\text { Is the process out of control? Explain. }$

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Definitions:

Element

A single-type atom substance characterized by its unique atomic number, the count of protons in its nucleus, defining it as a pure chemical element.

Electron Configuration

The distribution of electrons of an atom or molecule in atomic or molecular orbitals, influencing chemical bonds and properties.

Element

A substance that cannot be broken down into simpler substances by chemical means, consisting of atoms all with the same number of protons.

Electron Configuration

The arrangement of electrons in an atom or molecule within atomic or molecular orbitals.