Boxes of Honey-Nut Oatmeal are produced to contain 14.0 ounces, with a standard deviation of 0.10 ounce. For a sample size of 64 , the 3 -sigma $\bar{x}$ chart control limits are:
Upper Control Limit $\left(\mathrm{UCL}_{\bar{\chi}}^{-}\right)=14.04$ ounces (round your response to two decimal places).
Lower Control Limit $\left(\mathrm{LCL}_{\bar{x}}\right)=\square$ ounces (round your response to two decimal places).
Answer
Round the final answer to two decimal places: \(\boxed{13.96}\) ounces.
Step 1 ：Given that the mean (\(\bar{x}\)) is 14.0 ounces, the standard deviation (\(\sigma\)) is 0.10 ounce, and the sample size (\(n\)) is 64.
Step 2 ：The formula for the Lower Control Limit (LCL) in a \(\bar{x}\) chart is given by \(\bar{x} - 3\frac{\sigma}{\sqrt{n}}\).
Step 3 ：Substitute the given values into the formula: LCL = 14.0 - 3 * (0.10 / \(\sqrt{64}\))
Step 4 ：Calculate the value to get LCL = 13.9625
Step 5 ：Round the final answer to two decimal places: \(\boxed{13.96}\) ounces.
