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------------------------------------------------ The table below shows the times taken for a group of athletes to finish a 200 m race.

Work out the percentage of the athletes who took more than 26 seconds to finish the race.

[tex]
\[
\begin{tabular}{|c|c|}
\hline
\text{Time, } t(s) & \text{Frequency} \\
\hline
22 \ < \ t \leq 24 & 3 \\
\hline
24 \ < \ t \leq 26 & 5 \\
\hline
26 \ < \ t \leq 28 & 8 \\
\hline
28 \ < \ t \leq 30 & 9 \\
\hline
\end{tabular}
\]
[/tex]

Answer :

To solve the problem of finding the percentage of athletes who took more than 26 seconds to finish the 200 m race, follow these steps:

1. Identify the relevant intervals:
- We need to consider athletes who took more than 26 seconds. This includes the time intervals [tex]$26 < t \leq 28$[/tex] and [tex]$28 < t \leq 30$[/tex].

2. Count the number of athletes in each interval:
- For [tex]$26 < t \leq 28$[/tex], there are 8 athletes.
- For [tex]$28 < t \leq 30$[/tex], there are 9 athletes.

3. Add the number of athletes in these intervals:
- Total athletes taking more than 26 seconds = 8 (from [tex]$26 < t \leq 28$[/tex]) + 9 (from [tex]$28 < t \leq 30$[/tex]) = 17 athletes.

4. Find the total number of athletes:
- Sum the frequencies of all intervals:
- [tex]$22 < t \leq 24$[/tex]: 3 athletes
- [tex]$24 < t \leq 26$[/tex]: 5 athletes
- [tex]$26 < t \leq 28$[/tex]: 8 athletes
- [tex]$28 < t \leq 30$[/tex]: 9 athletes
- Total athletes = 3 + 5 + 8 + 9 = 25 athletes.

5. Calculate the percentage of athletes who took more than 26 seconds:
- Use the formula for percentage:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes who took more than 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
- Substitute the values into the formula:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]

Therefore, 68.0% of the athletes took more than 26 seconds to finish the race.