#### Answer

43% is the percentage of the students who sleep between 5 and 7 hours and 2% is the percentage of students who sleep between 9 and 11 hours.

#### Work Step by Step

Let us assume x to be the number of students who sleep between $5\,\,\text{ and }\,\,7$ hours and y to be the number of students who sleep between $9\,\,\text{ and }\,\,11$ hours..
The provided data can be represented in the form of the system of equations as follows:
$x+y=45$ (I)
$x-y=41$ (II)
Now add both of the equations above:
$\begin{align}
& \left( x+y \right)+\left( x-y \right)=\left( 41+45 \right) \\
& 2x=86 \\
& x=43
\end{align}$
Put the value of x in (II):
$\begin{align}
& x-y=41 \\
& 43-y=41 \\
& y=2
\end{align}$
Hence, the percentage of the students who sleep between 5 and 7 hours is 43% and the percentage of students who sleep between 9 and 11 hours is 2%.