Question

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 30 calories. Rosters 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).

Answer 1

UCL (x bar) = 424

LCL (x bar) = 376

Explanation:

Given:

Average calories contained, μ = 400

Standard deviation, σ = 30 calories

Sample size, n = 25

a) UCL (x bar) =
`\mu+(4\sigma)/(√(n))`

On substituting the respective values, we get

UCL (x bar) =
`400+(4*30)/(√(25))`

or

UCL (x bar) = 424

Similarly,

LCL (x bar) =
`\mu-(4\sigma)/(√(n))`

On substituting the respective values, we get

LCL (x bar) =
`400-(4*30)/(√(25))`

or

LCL (x bar) = 376