Question

A bookstore rents books to students at $2 per book. The cost per hour of running the bookstore is $300. The numbers of books and the probabilities that the bookstore would rent them in an hour mimics the distribution of the outcomes of flipping four coins. The number of books rented was observed to be the same as the number of heads that appear in a four-coin flip. This distribution is represented in the table.

No. of Heads Probability
0 1/16

1 4/16

2 6/16

3 4/16

4 1/16

Answer 1

Students usually rent four books a week during exams. The manager decides to charge a weekly fee of $6 for renting an unlimited number of books. Is this a fair decision for the students? Why? (Assume that fair in this case means that the students will save money.)

1)Yes, because students will pay less than it would cost them to rent four books.

2)No, because students will pay more than it would cost them to rent four books.

3)Yes, because students will break even.

4) No, because students will break even.

Answer 2

I figured it out. It's A.

Answer 3

The expected amount spent by a student is given by:
\[\large 0\times\frac{1}{16}+2\times\frac{4}{16}+4\times\frac{6}{16}+6\times\frac{4}{16}+8\times\frac{1}{16}\]
You need to calculate the expected amount spent. Then compare the expected amount with the weekly fee of $6 to find the correct choice of answer.