Q$12.$ A process has mean of $=25$ and S $=5.$ A sample size of $5$ is taken to control the process using Shewhart charts. Find the following$1.$ Using $3$ sigma Shewhart, find the UCL, and LCL $2.$ Find the average run length to receive a false signal when a process in control $($ie ARL $0)3.$ Repeat part $2$ using $2-$sigma Shewhart control chart $4.$ If the samples are collected every $2$ hour, find the average time to have a false signal $($your answer isbased on part $3)5.$ What will be the average length to detect a process shift to mean$=27$