1. **Problem Statement:** We have a frequency distribution of annual commission earnings (in thousands) for 150 salespeople. We want to find the proportion of salespeople earning less than $18,000. 2. **Understanding the Problem:** The data is grouped into intervals with frequencies. To find the proportion earning less than $18,000, we use an ogive (cumulative frequency graph) or cumulative frequency table. 3. **Constructing the Cumulative Frequency Table:** - Interval 0–5: Frequency = 6, Cumulative Frequency = 6 - Interval 5–10: Frequency = 12, Cumulative Frequency = 6 + 12 = 18 - Interval 10–15: Frequency = 15, Cumulative Frequency = 18 + 15 = 33 - Interval 15–20: Frequency = 35, Cumulative Frequency = 33 + 35 = 68 - Interval 20–25: Frequency = 40, Cumulative Frequency = 68 + 40 = 108 - Interval 25–30: Frequency = 23, Cumulative Frequency = 108 + 23 = 131 - Interval 30–35: Frequency = 11, Cumulative Frequency = 131 + 11 = 142 - Interval 35–40: Frequency = 8, Cumulative Frequency = 142 + 8 = 150 4. **Finding the cumulative frequency at $18,000:** - $18,000 lies in the 15–20 interval. - The cumulative frequency at 15 is 33. - The frequency for 15–20 is 35. - We assume uniform distribution within the interval. - The fraction of the interval from 15 to 18 is $\frac{18-15}{20-15} = \frac{3}{5}$. - So, cumulative frequency at 18 is $33 + 35 \times \frac{3}{5} = 33 + 21 = 54$. 5. **Calculating the proportion:** - Total salespeople = 150 - Proportion earning less than $18,000 = $\frac{54}{150} = 0.36$. 6. **Final answer:** About 36% of the salespeople earn less than $18,000 annually.