Final answer:
A process is typically considered out of control if a sample point falls more than three standard deviations from the process mean, based on the empirical rule for a bell-shaped distribution.
Step-by-step explanation:
When evaluating control processes and whether a sample is out of control, it's crucial to understand the role of standard deviations. Typically, a process is considered to be out of control if a sample point falls more than three standard deviations from the process mean. This is based on the empirical rule, which states that for a bell-shaped distribution, about 99.7% of data should fall within three standard deviations of the mean. If a point is beyond this range, it suggests that there may be some special cause of variation, rather than just random, common variation.
The empirical rule, particularly for a normally distributed set of data, indicates that if the process follows this distribution, we would expect approximately 68% of the data to fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Therefore, a difference greater than three standard deviations would suggest a process potentially being out of control. This would warrant further investigation into the cause of this variation.