Answer: 2.0

The 25th percentile is the value of $x$ for which $P(X \leq x)$ is greater than or equal to 0.25 and $P(X \geq x)$ is greater than or equal to 0.75. First, we need to find K. Since the probabilities must sum to 1: $$0.15 + 0.25 + 0.35 + K = 1$$ $$0.75 + K = 1$$ $$K = 0.25$$ Now we calculate cumulative probabilities: - $P(X \leq 1) = 0.15$ - $P(X \leq 2) = 0.15 + 0.25 = 0.40$ - $P(X \leq 3) = 0.15 + 0.25 + 0.35 = 0.75$ - $P(X \leq 4) = 1$ For the 25th percentile: - $P(X \leq 2) = 0.40 \geq 0.25$ - $P(X \geq 2) = 0.25 + 0.35 + 0.25 = 0.85 \geq 0.75$ Both conditions are satisfied for $x = 2$, so the 25th percentile is 2.0.

Author: Nikitesh Somanthe