The probability distribution of random variable X is given below: | X | 1 | 2 | 3 | 4 | 5 | | P(X)…

Given $P(X \le 2) = 0.28 \Rightarrow P(X = 1) + P(X = 2) = m + 3m = 4m = 0.28 \Rightarrow m = 0.07$. $P(X \ge 4) = 0.52 \Rightarrow P(X = 4) + P(X = 5) = 5m + b = 0.52 \Rightarrow 5(0.07) + b = 0.52 \Rightarrow b = 0.52 - 0.35 = 0.17$. Since the sum of all probabilities is 1: $\sum P(X) = m + 3m + a + 5m + b = 1 \Rightarrow 9m + a + b = 1$. Substituting $m = 0.07$ and $b = 0.17$: $9(0.07) + a + 0.17 = 1 \Rightarrow 0.63 + 0.17 + a = 1 \Rightarrow 0.80 + a = 1 \Rightarrow a = 0.2$. Therefore, $P(X = 3) = a = 0.2$.