Handout Assignment $2-$Topics $3$ and $4$

$1-$ A design engineer wants to construct a sample mean chart for controlling the service life of one of the types of light bulbs her company produces. She knows from numerous previous observations over many years that the output of the process is normally distributed with a mean service life of $700$ hours and a standard deviation of $30$ hours. On four recent production batches, she tested service life on random samples of ten bulbs.

a$)$ What is mean of sample means $($Grand mean$)?$

b$)$ What is the standard deviation of sampling distribution of sample mean?

c$)$ What are the lower control limit $($LCL$)$ and upper control limit $($UCL$)$ of the control chart $)=(3?$