The overall average on a process you are attending to monitor is $50$ units. The process standard deviation is $1\mathrm{.}72.$ Determine the upper and lower control limits for a mean chart, if you choose to use a sample size of $5.$ Set z$=3$ Problem $2$Pioneer Chicken advertise lite chicken with $30\%$ fewer calories than standard chicken. When the process for lite chicken breast productions is in control, the average chicken breast contains $420$ calories, and the standard deviation in caloric content of the chicken breast population is $25$ calories. Pioneer wants to design a mean chart to monitor the caloric content of chicken breasts, where $25$ chicken breasts would be chosen at random to form each sample. What are the lower and upper control limits for this chart if theses limits are chosen to be three standard deviations from the target?