College

The table below shows the times taken for a group of athletes to finish a 200 m race. Work out the percentage of the athletes who took more than 28 seconds to finish the race.

[tex]
\[
\begin{tabular}{|c|c|}
\hline
\text{Time, } t(s) & \text{Frequency} \\
\hline
24 < t \leq 26 & 3 \\
\hline
26 < t \leq 28 & 6 \\
\hline
28 < t \leq 30 & 9 \\
\hline
30 < t \leq 32 & 7 \\
\hline
\end{tabular}
\]
[/tex]

Answer :

Sure, let's solve the problem step by step:

1. Understand the Data: We have a table that shows how many athletes took certain time intervals to finish a 200 m race. The intervals are:
- 24 seconds < [tex]\( t \leq \)[/tex] 26 seconds: 3 athletes
- 26 seconds < [tex]\( t \leq \)[/tex] 28 seconds: 6 athletes
- 28 seconds < [tex]\( t \leq \)[/tex] 30 seconds: 9 athletes
- 30 seconds < [tex]\( t \leq \)[/tex] 32 seconds: 7 athletes

2. Determine Total Number of Athletes:
- We add up all the athletes in each interval to find the total number of athletes.
- Total = 3 (from 24-26s) + 6 (from 26-28s) + 9 (from 28-30s) + 7 (from 30-32s) = 25 athletes.

3. Identify Athletes Who Took More Than 28 Seconds:
- We're interested in those who took more than 28 seconds. So, we add the number of athletes who finished in the intervals 28-30 seconds and 30-32 seconds.
- More than 28 seconds = 9 (from 28-30s) + 7 (from 30-32s) = 16 athletes.

4. Calculate the Percentage:
- We need to find out what percentage of the total athletes took more than 28 seconds.
- Percentage = (Number of athletes who took more than 28 seconds / Total number of athletes) × 100
- Percentage = (16 / 25) × 100 = 64%

Therefore, 64% of the athletes took more than 28 seconds to finish the race.