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:

$\backslash$table$[[$Day$,$Weight$],[$Monday$,23,22,23,24],[$Tuesday$,23,21,19,21],[$Wednesday$,20,19,20,21],[$Thursday$,18,19,20,19],[$Friday$,18,20,22,20]]$

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$)?$

Multiple Choice

$0\mathrm{.}0026$

$0\mathrm{.}0456$

$0\mathrm{.}6826$

$0\mathrm{.}9544$

$0\mathrm{.}3174$