Mary Peterson is in charge of preparing blended flour for exotic bread making. The process is to take two different types of flour and mix them together in order to achieve high-quality breads. For one of the products, flour A and flour B are mixed together. The package of flour A comes from a packing process that has a population mean weight of 8 ounces with a population variance of 0.04.
The package of flour B has a population mean weight of 8 ounces and a population variance of 0.06. The package weights have a correlation of 0.40. The A and B packages are mixed together to obtain a 16-ounce package of special exotic flour. Every 60 minutes a random sample of four packages of exotic flour is selected from the process, and the mean weight for the four packages is computed.
Prepare a 99% acceptance interval for a quality-control chart for the sample means from the sample of four packages.
Show all your work and explain your reasoning. Explain how this acceptance chart would be used to ensure that the package weights continue to meet the standard.