(a) [2 marks]

\( W \sim N(204, 5^2) \).
EITHER
\( P(W > 210) = P\left(Z > \frac{210 – 204}{5}\right) = P(Z > 1.2) \approx 1 – 0.8849 \approx 0.1151 \approx 0.115 \) (M1A1).
OR
Sketch normal curve and identify area \( P(W > 210) \), compute \( z = 1.2 \), \( P(Z > 1.2) \approx 0.115 \) (M1A1).

(b) [2 marks]

EITHER
\( P(W < w) = 1 – P(w < W < 210) – P(W > 210) \) (M1).
\( P(w < W < 210) = 0.8 \), \( P(W > 210) \approx 0.1151 \).
\( P(W < w) = 1 – 0.8 – 0.1151 \approx 0.0849 \) (A1).
OR
Recognize \( P(w < W < 210) = 0.8 \), use \( P(W > 210) \approx 0.1151 \), compute \( P(W < w) = 1 – 0.8 – 0.1151 \approx 0.0849 \) (M1A1).

(c) [2 marks]

EITHER
\( P(W < w) \approx 0.0849 \), use inverse normal: \( z \approx -1.37 \) (M1).
\( w = 204 + (-1.37) \cdot 5 \approx 197.15 \approx 197 \) grams (A1).
OR
Sketch and use \( P(W < w) \approx 0.0849 \), find \( z \approx -1.37 \), compute \( w \approx 197 \) grams (M1A1).

(d) [2 marks]

EITHER
\( X \sim B(10, 0.0849) \) (M1).
\( P(X = 1) = \binom{10}{1} \cdot (0.0849)^1 \cdot (0.9151)^9 \approx 10 \times 0.0849 \times 0.4506 \approx 0.3821 \approx 0.382 \) (A1).
OR
Recognize binomial, compute \( P(X = 1) = 10 \cdot 0.0849 \cdot (0.9151)^9 \approx 0.382 \) (M1A1).