Using the Standard Error of the Sample Means to Calculate Control Limits}

In order to establish 2 -sigma control limits on the time it takes to complete an operation, a manager took random samples of four operator's performance every hour for five consecutive hours. The manager found that the overall average time of the operation is 30 minutes and the standard deviation of time is 3 minutes.

{Required:}
Determine the upper and lower control limits for the \(\mathrm{X}\) chart.