Complete the following Statistical Process Control problems:

$12345678910$

$109131012101013810$

$9991010101110812$

$1011101198108129$

$91110101112810128$

$121091010998912$

A process that is considered to be in control measures an ingredient in ounces. Below are the samples taken from the process. The population standard deviation is $1\mathrm{.}36.$

This image provides $10$ samples for a population.

If Z $=3,$ what are the control limits for the mean chart $($x$-$bar chart$)?$

What are the control limits for the range chart $($R chart$)?$

Is the process in control? Show your explanation.