Question

What would you need to know in order to calculate how many pre-1982 pennies and post-1982 pennies are in the mixed sample?

Answer 1

In 1982, the physical composition of the penny was changed; the ratio of the zinc to copper was essentially reversed. As a result, a pre-82 penny has a different density from a post-82 penny. It would help to know several things: first, the average mass and density of both a single pre and post 82 penny. Then you need to know how many pennies in total are in the mixed sample. You would also need to know the mass and density measures of "pure" samples, that is, if we have a mixed sample of 20 pennies, it would be useful to know the mass and density measurements of 20 pre-82 and 20 post-82 pennies. You can then figure out your estimate based on the variances in the density measurements.