Since vending machine use mass and size to differentiate between authentic and counterfeit coins, it is significant that coins be minted to close tolerances and that coins in circulation don't suffer significant changes in mass or size.

A thrifty chemistry instructor who is not reluctant to pick up a penny found on the street weighs 8 coins presumed to be pennies and recorded the given masses in gram: 2.5139, 3.1119, 2.5236, 2.4935, 2.5184, 2.4873, 2.5357 and 2.4948.

1) Before you proceed with the given calculations, examine the dataset. Should any data be rejected? Illustrate.

2) Estimate the average mass of a penny in circulation.

3) A parameter, in this case the average mass, is useless without an estimate of its uncertainty. Though we are only dealing with cents, it still makes sense to compute the given quantities: the standard deviation (standard deviation of a single measurement), the 95% confidence interval of a single measurement, the standard deviation of the mean and the 95% confidence interval of the mean. Report the mean with its 95% confidence interval to the correct number of significant digits.

4) Two coins are weighed. Coin A weighs 2.5307 g and coin B, 2.4210 g. Could either coin be a penny? Illustrate.

5) Assume that pennies were used as weights for balances. What would be the precision of the measurement of mass in this case?