Final answer:
The question discusses the normal distribution of assembly line workers' completion times, with a mean of 20 minutes and a standard deviation of 5 minutes, applying the 68-95-99.7 empirical rule to understand the probability of various time deviations.
Step-by-step explanation:
The question revolves around the concept of the normal distribution and standard deviation in a practical context. Specifically, it concerns the time necessary for assembly line workers to complete a product, which is normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes. When managing production lines, it is crucial to understand these statistics to predict and improve performance. Using the 68-95-99.7 empirical rule, also known as the three-sigma rule, we can state that approximately 68% of the data falls within one standard deviation of the mean (i.e., between 15 and 25 minutes for this case), about 95% falls within two standard deviations (i.e., between 10 and 30 minutes), and about 99.7% falls within three standard deviations (i.e., between 5 and 35 minutes). This rule helps in quality control and operational efficiencies by highlighting the probability of deviations from the expected completion time. Variations in these times can have significant implications for production planning and customer satisfaction.