Answer: 31.250%

To find the probability that the bond price is between $8.00 and $9.00, we need to integrate the probability density function over the interval [8, 9]: \[ P(8 \leq X \leq 9) = \int_{8}^{9} \left(\frac{x}{8} - 0.75\right) dx \] First, let's integrate: \[ \int \left(\frac{x}{8} - 0.75\right) dx = \frac{x^2}{16} - 0.75x + C \] Now evaluate from 8 to 9: \[ \left[\frac{9^2}{16} - 0.75 \times 9\right] - \left[\frac{8^2}{16} - 0.75 \times 8\right] \] \[ = \left[\frac{81}{16} - 6.75\right] - \left[\frac{64}{16} - 6\right] \] \[ = \left[5.0625 - 6.75\right] - \left[4 - 6\right] \] \[ = [-1.6875] - [-2] = -1.6875 + 2 = 0.3125 \] Converting to percentage: 0.3125 × 100% = 31.25% Therefore, the probability is 31.250%, which corresponds to option C.

Author: LeetQuiz Editorial Team