A process that is considered to be in control measures an ingredient in ounces. Below are the last $10$ samples

$($each of size n $=5)$ taken. The population process standard deviation, $\backslash$sigma is $1\mathrm{.}36.$

Samples

$12345678910$

$109131012101013810$

$9991010101110812$

$1011101198108129$

$91110101112810128$

$121091010998912$

a$)$ What is the standard deviation of the sampling means?

b$)$ If z $=3,$ what are the control limits for the mean chart?

c$)$ What are the control limits for the range chart?

d$)$ Is the process in control?