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 420 calories, and the standard deviation in caloric content of the chicken breast population is 25 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.

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

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ChiKesselman ChiKesselman · Answer 1 · 2020-03-25T18:15:21+01:00

Answer:

Lower control limit = 400 calories

Upper control limit = 440 calories

Step-by-step explanation:

We are given the following in the question:

Average calories in chicken breast = 420 calories.

Standard deviation of caloric content = 25 calories.

Sample size, n = 25

Limits are chosen to be four standard deviations from the target

Standard error =

[tex]=\dfrac{\sigma}{\sqrt{n}} = \dfrac{25}{\sqrt{25}} = 5[/tex]

Upper limit =

[tex]\mu + n\times \dfrac{\sigma}{\sqrt{n}}\\\\=420 + 4(5)\\=440[/tex]

The upper limit is 440 calories.

Lower limit =

[tex]\mu - n\times \dfrac{\sigma}{\sqrt{n}}\\\\=420 - 4(5)\\=400[/tex]

The lower limit is 400 calories.