(iii) Let the number of defective water pistols be a binomial random variable with parameters \(n = 1800\) and \(p = 0.08\).

Calculate \(np = 1800 \times 0.08 = 144\).

Calculate \(npq = 1800 \times 0.08 \times 0.92 = 132.48\).

Use a normal approximation: \(X \sim N(144, 132.48)\).

Apply continuity correction: \(P(X \geq 152) = P\left( Z > \frac{151.5 - 144}{\sqrt{132.48}} \right)\).

Calculate \(Z = \frac{151.5 - 144}{\sqrt{132.48}} = 0.6516\).

Find \(P(Z > 0.6516) = 1 - 0.7429 = 0.257\).

(iv) The approximation is justified because \(np = 1800 \times 0.08 = 144 > 5\) and \(n(1-p) = 1800 \times 0.92 = 1656 > 5\).