Answer :
Sure! Let's go through the solution step by step to find out what percentage of the athletes took more than 26 seconds to finish the race.
1. Identify the Time Intervals and Frequencies:
From the table, we can identify the following time intervals and the corresponding number of athletes (frequency) in each interval:
- [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:
To find the total number of athletes, we sum up all the frequencies:
[tex]\[
\text{Total athletes} = 3 + 5 + 8 + 9 = 25
\][/tex]
3. Determine the Number of Athletes Taking More Than 26 Seconds:
We are interested in those who took more than 26 seconds, which includes the intervals [tex]\(26 < t \leq 28\)[/tex] and [tex]\(28 < t \leq 30\)[/tex]. So, we add up the frequencies for these intervals:
[tex]\[
\text{Athletes above 26 seconds} = 8 + 9 = 17
\][/tex]
4. Calculate the Percentage:
Now, we calculate the percentage of athletes who took more than 26 seconds. This is done using the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes above 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
Plug the numbers in:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]
So, 68% of the athletes took more than 26 seconds to finish the race.
1. Identify the Time Intervals and Frequencies:
From the table, we can identify the following time intervals and the corresponding number of athletes (frequency) in each interval:
- [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:
To find the total number of athletes, we sum up all the frequencies:
[tex]\[
\text{Total athletes} = 3 + 5 + 8 + 9 = 25
\][/tex]
3. Determine the Number of Athletes Taking More Than 26 Seconds:
We are interested in those who took more than 26 seconds, which includes the intervals [tex]\(26 < t \leq 28\)[/tex] and [tex]\(28 < t \leq 30\)[/tex]. So, we add up the frequencies for these intervals:
[tex]\[
\text{Athletes above 26 seconds} = 8 + 9 = 17
\][/tex]
4. Calculate the Percentage:
Now, we calculate the percentage of athletes who took more than 26 seconds. This is done using the formula:
[tex]\[
\text{Percentage} = \left(\frac{\text{Number of athletes above 26 seconds}}{\text{Total number of athletes}}\right) \times 100
\][/tex]
Plug the numbers in:
[tex]\[
\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.0\%
\][/tex]
So, 68% of the athletes took more than 26 seconds to finish the race.
