A production process that is in control has a mean of $85$ and a standard deviation of $16.$

$($a$)$ Determine the upper and the lower control limits for a sample size of $30.($Round your answers to two decimal places.$)$

UCL $=$

$LCL=$

$($b$)$ Five samples had means of $82,85,93,88,$ and $86.$ Indicate whether or not the process is in control.

The process is in control.

The process is out of control.