The problem provides a dot plot summarizing the distance Roger ran in his tennis matches last month. Each dot represents one game. The question asks for a reasonable estimate of the probability that Roger runs less than 5 km in his next tennis match.

1. Problem Description

The problem provides a dot plot summarizing the distance Roger ran in his tennis matches last month. Each dot represents one game. The question asks for a reasonable estimate of the probability that Roger runs less than 5 km in his next tennis match.

2. Solution Steps

First, we need to determine the total number of tennis matches represented in the dot plot. We count the number of dots for each distance:

- 3 km: 1 dot

- 4 km: 2 dots

- 5 km: 4 dots

- 7 km: 2 dots

Total number of matches = 1 + 2 + 4 + 2 = 9

Next, we need to find the number of matches where Roger ran less than 5 km. This means we need to count the dots at 3 km and 4 km:

- 3 km: 1 dot

- 4 km: 2 dots

Number of matches less than 5 km = 1 + 2 = 3

The probability of Roger running less than 5 km in his next match is the number of matches less than 5 km divided by the total number of matches.

Probability = $\frac{\text{Number of matches less than 5 km}}{\text{Total number of matches}}$

Probability = $\frac{3}{9}$ = $\frac{1}{3}$

Now, we need to convert the fraction $\frac{1}{3}$ to a percentage.

$\frac{1}{3} \approx 0.3333$

$0.3333 \times 100\% = 33.33\%$

The closest answer to $33.33\%$ is $33\%$.

3. Final Answer

$33\%$