Quality control programs will often establish control limits that are three standard errors above and below a target mean for a process. A sample is taken from the process, and if the sample mean is within the control limits the process is deemed satisfactory. A process is designed to fill bottles with 16 ounces of soda with a standard deviation of 0.5 ounces.

a. Determine the control limits above and below the mean for this process using a sample size of 30.

b. What percentage of sample means would you expect to fall within these limits if the process is operating satisfactorily?