A Quality Analyst wants to construct a sample mean chart for controlling a packaging process. The analyst knows from past experience that whenever this process is under control, package weight is normally distributed with a mean of twenty ounces and a standard deviation of two ounces. Each day last week, the analyst randomly selected four packages and weighed each with the following results:

Day Weight $($ounces$)$

Monday $23222324$

Tuesday $23211921$

Wednesday $20192021$

Thursday $18192019$

Friday $18202220$

If upper and lower control limits of $23$ and $17$ ounces are used, what is his risk of concluding this process is in control when it is actually out of control $($Type II error$)?$

Question $29$ options:

$0\mathrm{.}0026$

$0\mathrm{.}0456$

$0\mathrm{.}3174$

$0\mathrm{.}6826$

$0\mathrm{.}9544$