30% of the residents of Wimfield own an electric car. Three residents are chosen at random.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. [M1] p³ +q³, p+q=1, p,q > 0 or 1-(3× p²xq+3×pxq²), p+q=1,p,q>0.
2. [A1] 0.37[0] or 37/100
3. [B1] 37.5 or 37½ and 26.25, 26½ seen, allow unsimplified. May be seen in standardisation formula. ([σ=]5.12, √105/2 implies correct variance).
4. [M1] Substituting their mean and their positive standard deviation into the standardising formula (any number for 45.5), not their σ², not their √σ.
5. [M1] Use continuity corrections 44.5 or 45.5 in their standardisation formula Note: +8/√26.25 or +8/5.123 seen gains M2 BOD
6. [M1] Appropriate area Φ, from final process, must be a probability. Expect final answer < 0.5. Note: appropriate final answer implies this M1.
7. [A1] 0.0592 < p < 0.0593.