The U.S. Bureau of Engraving and Printing produces $1, $5, $10, $20, $50, and $100 bills. The $2 banknote is still legal tender but is currently not in production. Each bill is designed to have the...

The U.S. Bureau of Engraving and Printing produces $1, $5, $10, $20, $50, and $100 bills. The $2 banknote is still legal tender but is currently not in production. Each bill is designed to have the same width, but many people perceive larger-denomination bills to be larger in size. Independent random samples of newly minted $1 and $20 bills were obtained, and the width of each (in mm) was recorded. The summary statistics are given in the following table.

Assume the underlying distributions are normal.