Answer: 3.0

**Step 1: Find the value of C** The sum of all probabilities must equal 1: $$C = 1 - 0.15 - 0.25 - 0.35 = 0.25$$ **Step 2: Determine the probabilities for each value** - $P(X=1) = 0.15$ - $P(X=2) = 0.25$ - $P(X=3) = 0.35$ - $P(X=4) = 0.25$ **Step 3: Identify the mode** The mode is the value with the highest probability. Comparing the probabilities: - $P(X=1) = 0.15$ - $P(X=2) = 0.25$ - $P(X=3) = 0.35$ (highest) - $P(X=4) = 0.25$ The value $x=3$ has the highest probability of 0.35. **Step 4: Conclusion** The mode of the distribution is $x=3$, which corresponds to option D (3.0).

Author: Nikitesh Somanthe