Question

If μ = 9 ounces, σ = 0.5 ounces, and n = 9, calculate the 3-sigma control limits for the x-bar chart.

Answer 1

For 3-sigma control limits for the x-bar chart Z = 3.

$UCL = μ + Z\frac{σ}{\sqrt{n}} \\ = 9 + 3\frac{0.5}{\sqrt{9}} \\ = 9.5 \\ LCL = μ - Z\frac{σ}{\sqrt{n}} \\ = 9 - 3\frac{0.5}{\sqrt{9}} \\ = 8.5$

Answer: 8.5 to 9.5 ounces