Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self$-$Destruction, an expos$$ on a famous politician's lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book's retail price is $$20,$ and the wholesale price is $$12.$ The publisher will buy back the retailer's leftover copies at a full refund, but McClure Books incurs $$4$ in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a normal distribution with a mean of $200$ and a standard deviation of $80.$ Table $13\mathrm{.}4$ is the standard normal table.

Note: If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specified method.

Dan will consider this book to be a blockbuster for him if it sells more than $400$ units. What is the probability that Power and Self$-$Destruction will be a blockbuster? Use Table $13\mathrm{.}4.$

Note: Round your answer to $4$ decimal places.

Dan considers a book a "dog" if it sells less than $50$ percent of his mean forecast. What is the probability this expose is a "dog"? Use Excel.

Note: Round your answer to $4$ decimal places.

What is the probability that demand for this book will be within $20$ percent of the mean forecast $($i$.$e$.,$ between $160$ and $240)?$ Use Table $13\mathrm{.}4.$

Note: Round your answer to $4$ decimal places.

What order quantity maximizes Dan's expected profit? Use Table $13\mathrm{.}4.$

If Dan orders the quantity needed to achieve a $95$ percent in$-$stock probability, what is the probability that some customer won't be able to purchase a copy of the book?

Note: Round your answer to $2$ decimal places.

Suppose Dan orders $300$ copies of the book. What is Dan's expected leftover inventory? Use Table $13\mathrm{.}4.$

Note: Round to the nearest whole number.

Suppose Dan orders $300$ copies of the book. What are Dan's expected sales? Use Table $13\mathrm{.}4.$

Note: Round to the nearest whole number.

Suppose Dan orders $300$ copies of the book. What is Dan's expected profit? Use Table $13\mathrm{.}4.$

Note: Round to the nearest whole number.

How many books should Dan order if he wants to achieve a $95$ percent in$-$stock probability? Use Table $13\mathrm{.}4.$