1. **State 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. **Recall the formula for frequency from a histogram:** $$\text{Frequency} = \text{Frequency density} \times \text{Class width}$$ This formula works because the area of each bar (height \(\times\) width) represents the frequency for that class. 3. **Identify the relevant classes and frequency densities:** - From 1 to 2 g: frequency density \(= 25\) - From 2 to 3 g: frequency density \(= 50\) 4. **Calculate the frequency for the part of the first class from 1.6 g to 2 g:** - Class width from 1 to 2 g is 1 g. - The portion from 1.6 to 2 g is \(2 - 1.6 = 0.4\) g. - Frequency estimate for this portion: $$25 \times 0.4 = 10$$ 5. **Calculate the frequency for the full class from 2 to 3 g:** - Class width is 1 g. - Frequency estimate: $$50 \times 1 = 50$$ 6. **Add the two frequencies to estimate the total number of rings between 1.6 g and 3 g:** $$10 + 50 = 60$$ 7. **Answer for part a):** Approximately 60 rings contain between 1.6 g and 3 g of gold. 8. **Answer for part b):** This is only an estimate because the histogram assumes frequency density is constant within each class interval, but the actual distribution of masses may vary within the intervals. Also, the exact number of rings is not given, only frequency densities, so we approximate by calculating areas under the bars.