Let's determine the percentage of students who scored at least 81 on the test by following these steps:
1. Identify the frequency of students in each score range:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Score} & \text{Frequency} \\
\hline 41-50 & 1 \\
\hline 51-60 & 2 \\
\hline 61-70 & 8 \\
\hline 71-80 & 12 \\
\hline 81-90 & 20 \\
\hline 91-100 & 7 \\
\hline
\end{array}
\][/tex]
2. Calculate the total number of students:
To find the total number of students, sum up all the frequencies:
[tex]\[
\begin{align*}
\text{Total number of students} &= 1 + 2 + 8 + 12 + 20 + 7 \\
&= 50
\end{align*}
\][/tex]
3. Determine the number of students who scored at least 81:
This includes students within the score ranges 81-90 and 91-100:
[tex]\[
\begin{align*}
\text{Students who scored at least 81} &= 20 + 7 \\
&= 27
\end{align*}
\][/tex]
4. Calculate the percentage of students who scored at least 81:
Use the formula for percentage:
[tex]\[
\text{Percentage} = \left( \frac{\text{Number of students who scored at least 81}}{\text{Total number of students}} \right) \times 100
\][/tex]
Substituting the numbers:
[tex]\[
\text{Percentage} = \left( \frac{27}{50} \right) \times 100 = 54.0\%
\][/tex]
Conclusion: The percentage of students who scored at least 81 on the test is [tex]\(54.0\%\)[/tex].
