Problem:

Dan McClure owns a thriving independent bookstore in Lawrence, Kansas. He must decide how many copies to order of a new book. Dan believes his demand forecast can be represented by a normal distribution with mean 200 and standard deviation 80.

Question 1) Dan will consider this book to be a "blockbuster" if it sells more than 350 units. What is the probability that this new book will be blockbuster?

Question 2) Dan will consider this book to be a "dog" if it sells less than 50% of his mean forecast. What is the probability that this new book will be a "dog"?

Question 3) What is the chance that the demand for the book is within 30% of the average value?

Question 4) Suppose that Dan's bookstore has 300 copies of this book and no other receipts are expected. How much is the expected lost sale?

Question 5) If Dan wants the expected lost sales of this book to be 2 books or lower, how many copies of the book should he order? (Please answer this question independent of part d above.)

Question 6) What order quantity should he choose to satisfy a 95% expected fill rate?

Question 7) How many books should Dan order if he wants to achieve a 95% in?stock probability?

Question 8) Even though the percentages for the expected fill rate and in?stock probability are the same, the order quantities differ. In a few sentences, explain the reason behind this difference (i.e., do your answers make sense?, which one is greater and why?, etc.).

Provide thorough explanation of every question given in the problem.