In Millford, 70% of the residents own a bicycle. A random sample of 160 residents is selected.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [B1] 112 and 33.6 (CAO) seen, allow un-simplified. May be in standardisation formula. (σ= √33.6,5.79655... to at least 4SF implies correct variance). Withold mark if variance clearly identified as standard deviation. Condone N(112, √33.6) if standardisation formula correct or variance/standard deviation stated correctly as well.
2. [M1] Substituting their 112 and their 33.6 into the standardising formula (any number for 120.5), allow σ² or √σ.
3. [M1] Use continuity correction 119.5 or 120.5 in their standardisation formula. Note: If no standardisation formula seen (8.5/√33.6) or ± (8.5/5.797) scores M2 BOD.
4. [M1] Appropriate area Φ, from final process, must be a probability. May be implied by a sketch of the required probability area. Note: correct final answer implies this M1. Expect final answer < 0.5.
5. [A1] Final answer AWRT.