Answer :
First, we identify the groups of athletes based on their finishing times. The intervals are:
- For times [tex]$24 < t \leq 26$[/tex], there are [tex]$3$[/tex] athletes.
- For times [tex]$26 < t \leq 28$[/tex], there are [tex]$6$[/tex] athletes.
- For times [tex]$28 < t \leq 30$[/tex], there are [tex]$9$[/tex] athletes.
- For times [tex]$30 < t \leq 32$[/tex], there are [tex]$7$[/tex] athletes.
We need to work out the percentage of athletes who took more than [tex]$28$[/tex] seconds to finish the race.
1. Calculate the total number of athletes by summing the frequencies:
[tex]$$
\text{Total athletes} = 3 + 6 + 9 + 7 = 25.
$$[/tex]
2. Identify which athletes took more than [tex]$28$[/tex] seconds. These are the athletes in:
- [tex]$28 < t \leq 30$[/tex] with [tex]$9$[/tex] athletes.
- [tex]$30 < t \leq 32$[/tex] with [tex]$7$[/tex] athletes.
So, the total number of athletes with times greater than [tex]$28$[/tex] s is:
[tex]$$
\text{Athletes over }28\text{ s} = 9 + 7 = 16.
$$[/tex]
3. Calculate the percentage:
[tex]$$
\text{Percentage} = \left(\frac{16}{25}\right) \times 100 = 64\%.
$$[/tex]
Thus, the percentage of athletes who took more than [tex]$28$[/tex] seconds to finish the race is [tex]$64\%$[/tex].
- For times [tex]$24 < t \leq 26$[/tex], there are [tex]$3$[/tex] athletes.
- For times [tex]$26 < t \leq 28$[/tex], there are [tex]$6$[/tex] athletes.
- For times [tex]$28 < t \leq 30$[/tex], there are [tex]$9$[/tex] athletes.
- For times [tex]$30 < t \leq 32$[/tex], there are [tex]$7$[/tex] athletes.
We need to work out the percentage of athletes who took more than [tex]$28$[/tex] seconds to finish the race.
1. Calculate the total number of athletes by summing the frequencies:
[tex]$$
\text{Total athletes} = 3 + 6 + 9 + 7 = 25.
$$[/tex]
2. Identify which athletes took more than [tex]$28$[/tex] seconds. These are the athletes in:
- [tex]$28 < t \leq 30$[/tex] with [tex]$9$[/tex] athletes.
- [tex]$30 < t \leq 32$[/tex] with [tex]$7$[/tex] athletes.
So, the total number of athletes with times greater than [tex]$28$[/tex] s is:
[tex]$$
\text{Athletes over }28\text{ s} = 9 + 7 = 16.
$$[/tex]
3. Calculate the percentage:
[tex]$$
\text{Percentage} = \left(\frac{16}{25}\right) \times 100 = 64\%.
$$[/tex]
Thus, the percentage of athletes who took more than [tex]$28$[/tex] seconds to finish the race is [tex]$64\%$[/tex].