Boxes of Honey-Nut Oatmeal are produced to contain 16.0 ounces, with a standard deviation of 0.15 ounce. For a sample size of 49 , the 3 -sigma \( \bar{x} \) chart control limits are: Upper Control Limit \( \left(\right. \) UCL \( \left._{\bar{x}}\right)=\square \) ounces (round your response to two decimal places). Lower Control Limit \( \left(\right. \) LCL \( \left._{\bar{x}}^{-}\right)=\square \) ounces (round your response to two decimal places).

To calculate the control limits for the \( \bar{x} \) chart using the given information, we can use the following formulas: 1. The Upper Control Limit (UCL) is calculated as: \[ UCL_{\bar{x}} = \mu + 3 \left(\frac{\sigma}{\sqrt{n}}\right) \] 2. The Lower Control Limit (LCL) is calculated as: \[ LCL_{\bar{x}} = \mu - 3 \left(\frac{\sigma}{\sqrt{n}}\right) \] Where: - \( \mu = 16.0 \) ounces (mean) - \( \sigma = 0.15 \) ounces (standard deviation) - \( n = 49 \) (sample size) First, calculate the standard error (SE): \[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.15}{\sqrt{49}} = \frac{0.15}{7} = 0.02142857 \] Now calculate UCL and LCL: \[ UCL_{\bar{x}} = 16.0 + 3(0.02142857) = 16.0 + 0.06428571 \approx 16.06 \text{ ounces} \] \[ LCL_{\bar{x}} = 16.0 - 3(0.02142857) = 16.0 - 0.06428571 \approx 15.94 \text{ ounces} \] Therefore, rounding to two decimal places: - Upper Control Limit (UCL) = **16.06 ounces** - Lower Control Limit (LCL) = **15.94 ounces**