Question

Pioneer 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 420 ​calories, and the standard deviation in caloric content of the chicken breast population is 20 calories. Pioneer wants to design an x overbar​-chart to monitor the caloric content of chicken​ breasts, where 25 chicken breasts would be chosen at random to form each sample. ​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? Upper Control Limit ​(UCL Subscript x overbar​)equals nothing calories ​(enter your response as an​ integer). Lower Control Limit ​(LCL Subscript x overbar​)equals nothing calories ​(enter your response as an​ integer). ​b) What are the limits with three standard deviations from the​ target? Upper Control Limit ​(UCL Subscript x overbar​)equals nothing calories ​(enter your response as an​ integer). Lower Control Limit ​(LCL Subscript x overbar​) ​= nothing calories ​(enter your response as an​ integer).  

Answer 1

a)

Standard error of mean = = 20 / = 4

Upper Control Limit​, UCL = = 420 + 4 * 4 = 436 calories

Lower Control Limit​, LCL = = 420 - 4 * 4 = 404 calories

b)

For limits with three standard deviations from the​ target,

Upper Control Limit​, UCL = = 420 + 3 * 4 = 432 calories

Lower Control Limit​, LCL = = 420 - 3 * 4 = 408 calories