Rosters Chicken advertises$$ "lite" chicken with$30\%$ fewer calories than standard chicken. When the process for$$ "lite" chicken breast production is in$$ control, the average chicken breast contains $400$calories$,$ and the standard deviation in caloric content of the chicken breast population is $25$ calories.

Rosters wants to design an x $-$chart to monitor the caloric content of chicken$$ breasts, where $25$ chicken breasts would be chosen at random to form each sample.

Part $2$

$$a$)$ What are the lower and upper control limits for this chart if these limits are chosen to be four standard deviations from the$$ target?

What are the limits with three standard deviations from the$$ target upper and lower control limit