Final answer:
For calculating the average mass of a penny, excluding data from damaged or unusual coins could provide a more accurate measurement for common circulation pennies. If the average is needed for practical applications like calibrating vending machines, options 1) and 4) are most suitable.
Step-by-step explanation:
When calculating the average mass of a penny, it's important to consider the purpose of the calculation. If you're determining the average for general circulation pennies, then excluding data from damaged pennies or pennies with unusual features could potentially give a more accurate representation of a regular penny's mass. Conversely, including all data, such as damaged coins or those with unusual features, might reflect the true variation found in circulation keys, but could skew the average if such pennies are not common. To get an average mass that represents what is typically encountered, particularly if this is for a practical application like calibrating a vending machine, option 1) and 4) would be reasonable choices.
The subject matter here is in the realm of statistics, a vital part of mathematics, involving the concepts of mean and standard deviation. Taking into account that the average weight of a coin is 5.201 g with a standard deviation of 0.065 g, we can assess the performance of a vending machine which accepts coins in a certain weight range. In this context, by applying the empirical rule or z-scores, we can estimate the number of coins likely to be rejected out of a sample, in this case, 280 coins.