Let's break down the given problem using the graph and the questions step by step. --- ## 1. **Fraction of Insects Between 10 and 12 Days** **Step 1: Read the graph values between 10 and 12 days.** - At 10 days, the density is approximately **0.10**. - At 12 days, the density is approximately **0.08**. **Step 2: Estimate the area (fraction) under the curve between 10 and 12 days.** - The interval is 2 days. - Average density: \((0.10 + 0.08)/2 = 0.09\) - Area ≈ \(0.09 \times 2 = 0.18\) **Step 3: Convert to a percentage (multiply by 100):** - \(0.18 \times 100 = 18\%\) **Answer:** **Between 10 and 12 days = 18%** --- ## 2. **Fraction Less Than 8 Days** **Step 1: Read graph values from 0 to 8 days.** - At 4 days: ~0.03 - At 6 days: ~0.06 - At 8 days: ~0.09 **Step 2: Estimate area from 4 to 8 days (since 0–4 is negligible):** - From 4 to 6 days (2 days, avg density ~0.045): \(2 \times 0.045 = 0.09\) - From 6 to 8 days (2 days, avg density ~0.075): \(2 \times 0.075 = 0.15\) - Total area ≈ \(0.09 + 0.15 = 0.24\) **Step 3: Convert to percentage:** - \(0.24 \times 100 = 24\%\) **Answer:** **Less than 8 days = 24%** --- ## 3. **Fraction More Than 10 Days** **Step 1: Estimate area under the curve from 10 days onward.** - From 10 to 12 days (already calculated): 0.18 - From 12 to 14 days: At 12 (~0.08), at 14 (~0.06), avg = 0.07, area = \(2 \times 0.07 = 0.14\) - From 14 to 16 days: At 14 (~0.06), at 16 (~0.03), avg = 0.045, area = \(2 \times 0.045 = 0.09\) - Sum: \(0.18 + 0.14 + 0.09 = 0.41\) **Step 2: Convert to percentage:** - \(0.41 \times 100 = 41\%\) **Answer:** **More than 10 days = 41%** --- ## 4. **Most Likely One-Day Interval** Look for the peak of the density function on the graph. - The peak is at **10 days** with the highest density (\(\approx 0.10\)). **Answer:** **One-day interval: 10 to 11 days** --- ## 5. **Most Likely Length of Larval Stage** - The larval stage is most likely between **10 and 11 days**, since that interval contains the peak. --- ## **Summary Table** | Question | Answer | |---------------------------------------------------------------|------------------| | Fraction between 10 and 12 days | 18% | | Fraction less than 8 days | 24% | | Fraction more than 10 days | 41% | | One-day interval most likely | 10 to 11 days | | Most likely length is between | 10 and 11 days | --- ### **Final Answers (to fill in boxes):** 1. **18** 2. **24** 3. **41** 4. **10** and **11** (days)