1. **State the problem:** We need to find the range of the giant panda's mass $p$ in grams at birth, given it is between $\frac{1}{950}$ and $\frac{1}{850}$ times its mother's mass, which is 95,950 grams. 2. **Write the inequality:** $$\frac{1}{950} \times 95,950 \leq p < \frac{1}{850} \times 95,950$$ 3. **Calculate the lower bound:** $$\frac{1}{950} \times 95,950 = \frac{95,950}{950} = 101$$ 4. **Calculate the upper bound:** $$\frac{1}{850} \times 95,950 = \frac{95,950}{850} = 112.88\overline{2} \approx 112.89$$ 5. **Write the final inequality:** $$101 \leq p < 112.89$$ 6. **Interpretation:** The giant panda's mass $p$ is predicted to be at least 101 grams but less than 112.89 grams. 7. **Match with options:** This corresponds to option B. **Final answer:** $$101 \leq p < 112.89$$