A Quality Analyst Wants to Construct a Sample Mean Chart

question 86

Multiple Choice

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is in control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each: $$\begin{array} { l l c c c } \text { Day } & &{ \text { Weight (ounces) } } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\text { Tuesday } & 23 & 21 & 19 & 21 \\\text { Wednesday } & 20 & 19 & 20 & 21 \\\text { Thursday } & 18 & 19 & 20 & 19 \\\text { Friday } & 18 & 20 & 22 & 20\end{array}$$
If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error) ?

• A) 0.0026
• B) 0.0456
• C) 0.3174
• D) 0.6826
• E) 0.9544

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Definitions:

Call Option

A financial contract that gives the holder the right, but not the obligation, to buy a specified amount of an underlying asset at a set price within a specific time frame.

American Option

A category of options agreement allowing execution at any moment prior to its expiry date.

European Option

A type of financial derivative that gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified price on the option's expiration date.

Exercise

In financial contexts, it refers to the act of invoking the right to buy or sell the underlying asset as specified in a derivatives contract, such as options or warrants.