Answer
$\displaystyle \left[\begin{array}{ll}
96\\
103\\
95
\end{array}\right]$
96 students with less than 4 hours of sleep
103 students with 4-7 hours of sleep
95 students with 7+ hours of sleep
Work Step by Step
$A=\displaystyle \left[\begin{array}{ll}
0.75 & 0.20 & 0.05\\
0.60 & 0.30 & 0.10\\
0.40 & 0.30 & 0.30
\end{array}\right]$
$B = \displaystyle \left[\begin{array}{ll}
80\\
170\\
40
\end{array}\right]$
Find the product matrix AB
$=\displaystyle \left[\begin{array}{ll}
0.75 * 80 + 0.20 * 170 + 0.05 * 40\\
0.60 * 80 + 0.30 * 170 + 0.10 * 40\\
0.40 * 80 + 0.30 * 170 + 0.30 * 40
\end{array}\right]$
$=\displaystyle \left[\begin{array}{ll}
60 + 34 + 2\\
48 + 51 + 4\\
32 + 51 + 12
\end{array}\right]$
$=\displaystyle \left[\begin{array}{ll}
96\\
103\\
95
\end{array}\right]$
96 students with less than 4 hours of sleep
103 students with 4-7 hours of sleep
95 students with 7+ hours of sleep
