Final answer:
A data point of 13.9 hits is 3.56 standard deviations above the mean of 10.2 hits in a normally distributed process. This falls outside the range predicted by the empirical rule, where over 99% of data should be within three standard deviations. Therefore, the process is considered out of control (Option A).
Step-by-step explanation:
When assessing whether a process is in control or out of control in the context of quality control, statisticians often apply the empirical rule in conjunction with control charts. The empirical rule states that for a bell-shaped and normally distributed set of data, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and over 99% within three standard deviations.
In the given scenario, the process has a mean of 10.2 hits per minute and a standard deviation of 1.04 hits per minute. When analyzing the data point of 13.9 hits, we calculate the number of standard deviations from the mean by subtracting the mean from the data point and then dividing by the standard deviation ((data point - mean) / standard deviation).
Applying this to the data point: (13.9 - 10.2) / 1.04 = 3.56. The resulting value of 3.56 indicates that this point is more than three standard deviations above the mean, placing it outside the range predicted by the empirical rule. According to commonly accepted quality control practices, data points more than three standard deviations from the mean suggest that a process might be out of control.
The final answer is Option A: Out of control as this one data point is more than three standard deviations from the mean, suggesting that the process needs to be investigated for potential issues.