An X Chart Based on Standard Deviations (Instead of Ranges)

question 19

Essay

An x chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline
at x and control limits at x + A3 s and x - A3 s where A3 is found in the Control Chart Constants table and s is
the mean of the sample standard deviations. Construct an x chart based on standard deviations for the data
below.
A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality
control. The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated.
The results for 12 consecutive days are shown in the table below. $$\begin{array} { c | c | c | c } \text { Day } & \bar { x } & \text { Range } & \mathrm { s } \\\hline 1 & 21.1 & 3.4 & 1.2 \\2 & 23.4 & 4.7 & 1.7 \\3 & 20.9 & 3.1 & 0.9 \\4 & 25.6 & 6.2 & 2.3 \\5 & 21.3 & 4.7 & 1.3 \\6 & 20.5 & 3.7 & 1.7 \\7 & 25.8 & 5.8 & 2.1 \\8 & 23.7 & 6.2 & 2.9 \\9 & 29.8 & 2.1 & 0.8 \\10 & 22.7 & 4.4 & 1.6 \\11 & 20.0 & 2.7 & 0.7 \\12 & 24.6 & 7.8 & 3.0\end{array}$$

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Definitions:

Sensory Neurons

Nerve cells that are responsible for converting external stimuli from the environment into corresponding internal stimuli, allowing for the perception of sensory information.

Central Nervous System

The part of the nervous system that consists of the brain and spinal cord, functioning as the primary control center for processing and sending out information.

Motor Neurons

Nerve cells that transmit impulses from the central nervous system to muscles or glands, enabling movement and action.

Central Nervous System

The part of the nervous system consisting of the brain and spinal cord, responsible for processing and transmitting information.