Answer: 200

## Explanation For a uniform distribution on the interval [0,500], the probability density function is: \[ f(x) = \frac{1}{500 - 0} = \frac{1}{500} \] ### Finding the Median (50th percentile) The median is found by solving: \[ P(X < k) = (k - 0) \cdot f(x) = 0.5 \] \[ \Rightarrow \frac{1}{500}k = 0.5 \] \[ \Rightarrow k = 0.5 \times 500 = 250 \] ### Finding the 10th percentile The 10th percentile is found by solving: \[ P(X < k) = (k - 0) \cdot f(x) = 0.10 \] \[ \Rightarrow \frac{1}{500}k = 0.10 \] \[ \Rightarrow k = 0.10 \times 500 = 50 \] ### Calculating the Difference \[ \text{Difference} = \text{Median} - \text{10th percentile} = 250 - 50 = 200 \] Therefore, the correct answer is **B. 200**.

Author: Tanishq Prabhu