1. **Stating the problem:** We need to estimate the number of rings containing between 1.6 g and 3 g of gold using the histogram data. 2. **Understanding the histogram:** The histogram shows frequency density on the y-axis and mass intervals on the x-axis. The frequency (number of rings) for an interval is calculated by multiplying the frequency density by the width of the interval. 3. **Formula:** $$\text{Frequency} = \text{Frequency density} \times \text{Class width}$$ 4. **Calculate frequency for 1.6 g to 2 g:** - Frequency density between 1 and 2 g is about 40. - Class width from 1.6 to 2 is $2 - 1.6 = 0.4$. - Frequency $= 40 \times 0.4 = 16$. 5. **Calculate frequency for 2 g to 3 g:** - Frequency density between 2 and 3 g is about 25. - Class width is $3 - 2 = 1$. - Frequency $= 25 \times 1 = 25$. 6. **Total estimated frequency between 1.6 g and 3 g:** $$16 + 25 = 41$$ rings. 7. **Explanation why this is an estimate:** The value is an estimate because the histogram groups data into intervals and assumes uniform distribution of rings within each interval. The exact number of rings between 1.6 g and 2 g is approximated by scaling the frequency density, which may not reflect the true distribution. **Final answer:** Approximately 41 rings contain between 1.6 g and 3 g of gold.