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If the sample average double overbar(x) = 23 ounces, and the population standard deviation σ = 1.0 ounces, and the sample size n = 16, what will be the ± 3σ control limits for the x-bar chart?

A. 22.70 to 23.30 ounces
B. 21.8 to 24.2 ounces
C. 23 ounces
D. 22.90 to 23.10 ounces
E. 22.25 to 23.75 ounces

1 Answer

4 votes

Final answer:

The ± 3σ control limits for the x-bar chart, given the sample average of 23 ounces, population standard deviation of 1.0 ounces, and sample size of 16, are calculated as 23 ± 0.75, which yields control limits of 22.25 to 23.75 ounces.

Step-by-step explanation:

The question asks for the ± 3σ control limits for the x-bar chart, given the sample average ¯x = 23 ounces, the population standard deviation σ = 1.0 ounces, and the sample size n = 16. Since the ¯x chart is based on the sampling distribution of the mean, the standard deviation of the sample mean, known as the standard error, is σ/√n. The control limits are then calculated as:

  • ¯x ± zσ/√n
  • ¯x ± 3*(1.0)/√16
  • ¯x ± 3*(1.0)/4
  • ¯x ± 3*0.25
  • ¯x ± 0.75
  • 23 ± 0.75
  • 22.25 to 23.75 ounces

So, the correct answer is E. 22.25 to 23.75 ounces.

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