1. **Problem:** Let $X$ be binomial with $n=25$, $p=0.2$. Find $P(X < \mu_x - 2\sigma_x)$. 2. **Formulas:** For binomial, $\mu_x = np$, $\sigma_x = \sqrt{np(1-p)}$. 3. **Calculate mean and std dev:** $\mu_x = 25 \times 0.2 = 5$ $\sigma_x = \sqrt{25 \times 0.2 \times 0.8} = \sqrt{4} = 2$ 4. **Find cutoff:** $\mu_x - 2\sigma_x = 5 - 2 \times 2 = 1$ 5. **Calculate probability:** $P(X < 1) = P(X \leq 0)$ since $X$ is discrete. 6. **Evaluate:** $P(X=0) = (1-p)^n = 0.8^{25} \approx 0.0032$ **Answer:** $P(X < \mu_x - 2\sigma_x) \approx 0.0032$