To determine the best seating section for Leanne's family to maximize their chances of having a "perfect" view of the symphony's soloist, we need to analyze the data given for each section. The relevant data includes the number of reviewers in each section and the number of those reviewers who rated the view as "perfect."
Here is the data presented:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Section} & \text{Number of Reviewers} & \text{Number of Perfect Ratings} \\
\hline
L1 & 90 & 57 \\
\hline
L2 & 52 & 33 \\
\hline
L3 & 75 & 47 \\
\hline
U1 & 84 & 55 \\
\hline
U2 & 43 & 27 \\
\hline
U3 & 35 & 22 \\
\hline
\end{array}
\][/tex]
To find out which section has the highest chances of giving a "perfect" view, we need to calculate the ratio of "perfect" reviews to the total number of reviewers for each section. This ratio can be found using the following formula:
[tex]\[
\text{Ratio} = \frac{\text{Number of Perfect Ratings}}{\text{Number of Reviewers}}
\][/tex]
Let's calculate the ratio for each section:
Section L1:
[tex]\[
\text{Ratio} = \frac{57}{90} \approx 0.6333
\][/tex]
Section L2:
[tex]\[
\text{Ratio} = \frac{33}{52} \approx 0.6346
\][/tex]
Section L3:
[tex]\[
\text{Ratio} = \frac{47}{75} \approx 0.6267
\][/tex]
Section U1:
[tex]\[
\text{Ratio} = \frac{55}{84} \approx 0.6548
\][/tex]
Section U2:
[tex]\[
\text{Ratio} = \frac{27}{43} \approx 0.6279
\][/tex]
Section U3:
[tex]\[
\text{Ratio} = \frac{22}{35} \approx 0.6286
\][/tex]
Now, let's compare these ratios:
- L1: [tex]\(0.6333\)[/tex]
- L2: [tex]\(0.6346\)[/tex]
- L3: [tex]\(0.6267\)[/tex]
- U1: [tex]\(0.6548\)[/tex]
- U2: [tex]\(0.6279\)[/tex]
- U3: [tex]\(0.6286\)[/tex]
We observe that Section U1 has the highest ratio of [tex]\(0.6548\)[/tex].
Therefore, Leanne's family should book their tickets in Section U1 to maximize their chances of having a "perfect" view of the symphony's soloist.
