Anil is a candidate in an election. He received 40% of the votes. A random sample of 120 voters is chosen. Use an approximation to find the probability that, of the 120 voters, between 36 and 54 inclusive voted for Anil.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] Mean = 120 × 0.4 = 48
2. [B1] Var = 120 × 0.4 × 0.6 = 28.8
3. [B1] 48 and 28.8 seen, allow unsimplified.
4. [B1] (5.366 < σ ≤ 5.367 or 12√5/5 implies correct variance).
5. [M1] Substituting their μ and σ into one standardisation formula (any number for 35.5 or 54.5), condone σ² and √σ.
6. [M1] Using continuity correction 35.5, 36.5 or 53.5, 54.5 once in their standardisation formula.
7. [M1] Note: ±12.5/√28.8 or ±6.5/√28.8 seen gains M2 BOD.
8. [M1] Appropriate area Φ, from final process. Must be a probability. Expect final answer > 0.5 .
9. [M1] Note: correct final answer implies this M1.
10. [A1] 0.877 ≤ p < 0.8772 .