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:

Day Weight $($ounces$)$

Monday $23222324$

Tuesday $23211921$

Wednesday $20192021$

Thursday $18192019$

Friday $18202220$

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

$0\mathrm{.}9544$

$0\mathrm{.}6826$

$0\mathrm{.}0026$

$0\mathrm{.}3174$

$0\mathrm{.}0456$