A Manufacturer of Lightbulbs Picks 10 Lightbulbs at Random Each

Multiple Choice

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean and range (in hours) of the lifetimes of the 10 lightbulbs are calculated. The results for
12 consecutive days are shown in the table below. Construct an R chart to determine whether
The process is in statistical control.
$\begin{array}{c|c|c|c}\text { Day } & \bar{x} & \text { Range } & s \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3 \\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\end{array}$

$\text { Control Chart Constants }$

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

A) $\text { The process is within statistical control. }$
B) $\text { The process is not within statistical control. }$