Answer :
To find the percentage of athletes who took more than 26 seconds to finish the race, follow these steps:
1. Identify the frequency of athletes in each time interval:
- For the time interval [tex]\(22 < t \leq 24\)[/tex], there are 3 athletes.
- For the time interval [tex]\(24 < t \leq 26\)[/tex], there are 5 athletes.
- For the time interval [tex]\(26 < t \leq 28\)[/tex], there are 8 athletes.
- For the time interval [tex]\(28 < t \leq 30\)[/tex], there are 9 athletes.
2. Calculate the total number of athletes:
- Add all the frequencies together: [tex]\(3 + 5 + 8 + 9 = 25\)[/tex]. So, there are 25 athletes in total.
3. Determine the number of athletes who took more than 26 seconds:
- This includes athletes in the time intervals [tex]\(26 < t \leq 28\)[/tex] and [tex]\(28 < t \leq 30\)[/tex].
- Add these frequencies: [tex]\(8 + 9 = 17\)[/tex]. There are 17 athletes who took more than 26 seconds.
4. Calculate the percentage of these athletes:
- Use the formula for percentage: [tex]\(\left(\frac{\text{Number of athletes taking more than 26 s}}{\text{Total number of athletes}}\right) \times 100\)[/tex].
- Substitute the values: [tex]\(\left(\frac{17}{25}\right) \times 100 = 68\%\)[/tex].
Thus, 68% of the athletes took more than 26 seconds to finish the race.
1. Identify the frequency of athletes in each time interval:
- For the time interval [tex]\(22 < t \leq 24\)[/tex], there are 3 athletes.
- For the time interval [tex]\(24 < t \leq 26\)[/tex], there are 5 athletes.
- For the time interval [tex]\(26 < t \leq 28\)[/tex], there are 8 athletes.
- For the time interval [tex]\(28 < t \leq 30\)[/tex], there are 9 athletes.
2. Calculate the total number of athletes:
- Add all the frequencies together: [tex]\(3 + 5 + 8 + 9 = 25\)[/tex]. So, there are 25 athletes in total.
3. Determine the number of athletes who took more than 26 seconds:
- This includes athletes in the time intervals [tex]\(26 < t \leq 28\)[/tex] and [tex]\(28 < t \leq 30\)[/tex].
- Add these frequencies: [tex]\(8 + 9 = 17\)[/tex]. There are 17 athletes who took more than 26 seconds.
4. Calculate the percentage of these athletes:
- Use the formula for percentage: [tex]\(\left(\frac{\text{Number of athletes taking more than 26 s}}{\text{Total number of athletes}}\right) \times 100\)[/tex].
- Substitute the values: [tex]\(\left(\frac{17}{25}\right) \times 100 = 68\%\)[/tex].
Thus, 68% of the athletes took more than 26 seconds to finish the race.
