Answer :
We are given the number of athletes finishing the race in the following time intervals:
- For [tex]$22 < t \leq 24$[/tex] seconds: 3 athletes
- For [tex]$24 < t \leq 26$[/tex] seconds: 5 athletes
- For [tex]$26 < t \leq 28$[/tex] seconds: 8 athletes
- For [tex]$28 < t \leq 30$[/tex] seconds: 9 athletes
Since we need the percentage of athletes who took more than 26 seconds to finish, we consider the athletes in the intervals [tex]$26 < t \leq 28$[/tex] and [tex]$28 < t \leq 30$[/tex].
1. First, add the frequencies of these intervals:
[tex]$$\text{Number of athletes with } t > 26 = 8 + 9 = 17.$$[/tex]
2. Next, calculate the total number of athletes by summing all the given frequencies:
[tex]$$\text{Total number of athletes} = 3 + 5 + 8 + 9 = 25.$$[/tex]
3. Now, determine the percentage using the formula:
[tex]$$\text{Percentage} = \left(\frac{\text{Number of athletes with } t > 26}{\text{Total number of athletes}}\right)\times 100.$$[/tex]
Substituting the values, we get:
[tex]$$\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.$$[/tex]
Hence, the percentage of athletes who took more than 26 seconds to finish the race is [tex]$$\boxed{68\%}.$$[/tex]
- For [tex]$22 < t \leq 24$[/tex] seconds: 3 athletes
- For [tex]$24 < t \leq 26$[/tex] seconds: 5 athletes
- For [tex]$26 < t \leq 28$[/tex] seconds: 8 athletes
- For [tex]$28 < t \leq 30$[/tex] seconds: 9 athletes
Since we need the percentage of athletes who took more than 26 seconds to finish, we consider the athletes in the intervals [tex]$26 < t \leq 28$[/tex] and [tex]$28 < t \leq 30$[/tex].
1. First, add the frequencies of these intervals:
[tex]$$\text{Number of athletes with } t > 26 = 8 + 9 = 17.$$[/tex]
2. Next, calculate the total number of athletes by summing all the given frequencies:
[tex]$$\text{Total number of athletes} = 3 + 5 + 8 + 9 = 25.$$[/tex]
3. Now, determine the percentage using the formula:
[tex]$$\text{Percentage} = \left(\frac{\text{Number of athletes with } t > 26}{\text{Total number of athletes}}\right)\times 100.$$[/tex]
Substituting the values, we get:
[tex]$$\text{Percentage} = \left(\frac{17}{25}\right) \times 100 = 68.$$[/tex]
Hence, the percentage of athletes who took more than 26 seconds to finish the race is [tex]$$\boxed{68\%}.$$[/tex]
