1. **Problem statement:** We need to estimate the number of rings containing between 1.4 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 area of each bar (width × height) gives the frequency (number of rings) in that mass range. 3. **Formula:** Frequency = Frequency density × Class width 4. **Step-by-step calculation:** - From 1.4 g to 2 g: The bar from 1 to 2 g has height 25. - Class width = 2 - 1.4 = 0.6 - Frequency = 25 × 0.6 = 15 - From 2 g to 3 g: The histogram shows two bars within this interval, one low at about 30 and one high at about 75. Since the problem states a histogram, these likely represent two sub-intervals (e.g., 2 to 2.5 and 2.5 to 3). We estimate frequencies for each: - For 2 to 2.5 g (width 0.5), height about 30: Frequency = 30 × 0.5 = 15 - For 2.5 to 3 g (width 0.5), height about 75: Frequency = 75 × 0.5 = 37.5 - Total frequency from 1.4 to 3 g = 15 + 15 + 37.5 = 67.5 5. **Interpretation:** Since frequency must be whole rings, we estimate about 68 rings. 6. **Answer to part b:** This is only an estimate because the histogram groups data into intervals and assumes uniform distribution within each bar. Also, the exact heights and boundaries are approximated from the graph, so the true number may vary. **Final answer:** Approximately 68 rings contain between 1.4 g and 3 g of gold.