Final answer:
The mean diameter of cans on an assembly line calculated from the given diameters is approximately 5.4, not 5.5. Mean, distributions, and standard deviation are essential concepts in statistics for understanding and analyzing data in various quality control scenarios.
Step-by-step explanation:
The student is asking about the mean diameter of cans measured on an assembly line. To calculate the mean diameter, you would add up all the given diameters and then divide by the number of cans. However, the provided mean of 5.5 does not match this calculation based on the given diameters (5.8, 5.2, 5.2, 5.3, 5.2, 5.5, 5.8, 5.5, 5.1). When you calculate the correct mean diameter, it is actually approximated to 5.4.
In mathematical statistics, this concept is vital in understanding distributions and sampling. For instance, when we apply the central limit theorem to a uniform distribution of screw diameters with a given range, we would predict that the distribution of the sample means will approach a normal distribution as the sample size grows.
Similarly, in the context of quality control such as checking the weight of cereal boxes or the volume of cough syrup dispensed by machines, standard deviation is a critical factor in determining the need for recalibration or checking for precision and accuracy.