A Machine That Is Supposed to Fill Small Bottles to Contain

question 122

Multiple Choice

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour. What would be the centerline for a control chart for $\bar { x }$ ?
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Bottle Volume (mL) }$
$\begin{array}{c|cccc|c|c}\text { Sample }&&&&&\bar{x}&\text { Range }\\\hline1 & 19.9 & 20.1 & 20.2 & 20.3 & 20.125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.250 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.350 & 0.7 \\4 & 20.4 & 20.1 & 20.1 & 19.9 & 20.125 & 0.5 \\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.700 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7 & 19.525 & 0.3 \\7 & 19.8 & 19.4 & 19.6 & 19.7 & 19.625 & 0.4 \\8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925 & 0.2 \\9 & 20.2 & 20.3 & 20.1 & 20.3 & 20.225 & 0.2 \\10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125 & 0.3 \\11 & 20.3 & 20.5 & 20.1 & 20.2 & 20.275 & 0.4 \\12 & 20.1 & 19.9 & 19.8 & 19.7 & 19.875 & 0.4 \\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.650 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.400 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.650 & 0.4\end{array}$

• A) \(0.380\) milliliters
• B) \(19.935\) milliliters
• C) \(20.000\) milliliters
• D) \(20.212\) milliliters

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Definitions:

Replenishment Lead Time

The time interval between placing an order and receiving the stock, crucial for inventory management.

Product Availability

The degree to which products are in stock and readily available to meet customer demand.

Supply Chain Coordination

The alignment and harmonization of strategies and actions among all participants in a supply chain to improve efficiency and effectiveness.

Replenishment Lead Time

The time taken from placing an order for more inventory until it is received and ready for use or sale, impacting inventory management strategies.