1. The problem is to calculate the sample size $n$ using the formula: $$n = \frac{Z^2 \times p \times q}{e^2}$$ where $Z = 1.96$, $p = 0.247$, $q = 1 - p = 1 - 0.247 = 0.753$, and $e = 0.05$. 2. Substitute the values into the formula: $$n = \frac{(1.96)^2 \times 0.247 \times 0.753}{(0.05)^2}$$ 3. Calculate each part step-by-step: - Calculate $Z^2$: $1.96^2 = 3.8416$ - Calculate $p \times q$: $0.247 \times 0.753 = 0.186\,091$ - Calculate $e^2$: $0.05^2 = 0.0025$ 4. Now substitute these values back: $$n = \frac{3.8416 \times 0.186091}{0.0025}$$ 5. Multiply numerator: $$3.8416 \times 0.186091 = 0.7149$$ 6. Divide by denominator: $$n = \frac{0.7149}{0.0025} = 285.96$$ 7. Since sample size must be a whole number, round up: $$n = 286$$ **Final answer:** The required sample size is $286$.