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. Understand the Frequency Table:
- The table provides the number of athletes who finished the race within specific time intervals. The intervals and their corresponding frequencies are:
- [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
2. Calculate the Total Number of Athletes:
- Add up the frequencies to find the total number of athletes.
- Total athletes = 3 + 5 + 8 + 9 = 25 athletes
3. Identify the Number of Athletes More Than 26 Seconds:
- Look at the intervals where the time is more than 26 seconds:
- [tex]\(26 < t \leq 28\)[/tex]: 8 athletes
- [tex]\(28 < t \leq 30\)[/tex]: 9 athletes
- Add these frequencies to get the total number of athletes who took more than 26 seconds.
- Athletes more than 26 seconds = 8 + 9 = 17 athletes
4. Calculate the Percentage:
- To find the percentage of athletes who took more than 26 seconds, use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes more than 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
- Substitute the values:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]
Therefore, 68% of the athletes took more than 26 seconds to finish the 200 m race.
1. Understand the Frequency Table:
- The table provides the number of athletes who finished the race within specific time intervals. The intervals and their corresponding frequencies are:
- [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
2. Calculate the Total Number of Athletes:
- Add up the frequencies to find the total number of athletes.
- Total athletes = 3 + 5 + 8 + 9 = 25 athletes
3. Identify the Number of Athletes More Than 26 Seconds:
- Look at the intervals where the time is more than 26 seconds:
- [tex]\(26 < t \leq 28\)[/tex]: 8 athletes
- [tex]\(28 < t \leq 30\)[/tex]: 9 athletes
- Add these frequencies to get the total number of athletes who took more than 26 seconds.
- Athletes more than 26 seconds = 8 + 9 = 17 athletes
4. Calculate the Percentage:
- To find the percentage of athletes who took more than 26 seconds, use the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes more than 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
- Substitute the values:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]
Therefore, 68% of the athletes took more than 26 seconds to finish the 200 m race.
