Previous
Clever | Portal
3
A bookstore rents books to students for $\$ 2$ per book. The cost of running the bookstore is $\$ 300$ per hour. 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 probability of renting a number of books 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.
\begin{tabular}{|c|c|}
\hline Books Rented & Probability \\
\hline 0 & $\frac{1}{16}$ \\
\hline 1 & $\frac{4}{16}$ \\
\hline 2 & $\frac{6}{16}$ \\
\hline 3 & $\frac{4}{16}$ \\
\hline 4 & $\frac{1}{16}$ \\
\hline
\end{tabular}
If its only income came from book rentals, the bookstore would have to rent books to students each hour, on average, to break even.
Reset
Next
c) 2023 Edmentum. All rights reserved.
Answer
Final Answer: The bookstore would have to rent \(\boxed{75}\) books to students each hour, on average, to break even.
Step 1 ：The bookstore needs to cover its running cost of $300 per hour. The income from each book rented is $2. Therefore, we need to find the expected number of books rented per hour to cover the cost.
Step 2 ：The expected value (E) of a random variable is given by the sum of the product of each outcome and its probability. In this case, the outcome is the number of books rented and the probability is given in the table.
Step 3 ：Using the given probabilities and the number of books, we calculate the expected value (E) to be 2.0.
Step 4 ：To break even, the bookstore would need to rent out 75 books per hour on average.
Step 5 ：Final Answer: The bookstore would have to rent \(\boxed{75}\) books to students each hour, on average, to break even.
