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.