The campus bookstore knows from the past several semesters that a certain elementary statistics book has a demand that is approximated by a normal distribution with a mean of 250 and a standard deviation of 40.They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each.All demand for this book is realized by the middle of the semester, at which point the bookstore bundles them up and sells them to a vendor in another country for $40 each.What is the marginal loss for a single elementary statistics book?
A)$40
B)$65
C)$105
D)$117

Question

Quizplus · Accepted Answer

To find the marginal loss, we need to find the difference between the revenue of selling the book at the initial price and the cost of selling it to the vendor later.

Revenue from selling each book = $222
Cost of buying each book = $105
Cost of selling each book to vendor = $40

We know that the demand for the book follows a normal distribution with mean 250 and standard deviation 40. To find the probability that the demand is less than or equal to the supply (1 book), we need to standardize:

Z = (x - mu) / sigma
Z = (1 - 250) / 40
Z = -6.225

Using a standard normal distribution table, the probability of Z being less than or equal to -6.225 is essentially 0. This means that the probability of the bookstore not selling all of its inventory is almost 0.

Therefore, the marginal loss for a single book is the difference between the initial revenue and the cost of selling to the vendor:

Marginal loss = Revenue - Cost of selling to vendor
Marginal loss = $222 - $40
Marginal loss = $182

However, we have to remember that the cost of buying the book is $105 each. This means that even if the book is sold to the vendor, the bookstore is still making a profit:

Profit = Revenue - Cost 
Profit = $40 - $105
Profit = -$65

This negative profit is only a marginal loss if we take into account the initial revenue earned. Therefore, the marginal loss for a single elementary statistics book is $222 - $105 - $40 = $77. This means that even with the loss of selling the book to the vendor, the bookstore still makes a profit of $77 per book.

The Campus Bookstore Knows from the Past Several Semesters That