$1.($Returning books$)$ Dan McClure is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season for his bookstore. The book retails at $$28\mathrm{.}00.$ The publisher sells the book to Dan for $$20\mathrm{.}00.$ Dan will dispose of all of the unsold copies of the book at $75$ percent off the retail price, at the end of the season. Dan estimates that demand for this book during the season is normal with a mean of $100$ and a standard deviation of $42.$