In a certain area in the Arctic the probability that it snows on any given day is 0.7, independent of all other days.

Mark scheme

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

1. [M1] One term nCx (p)^x (1-p)^(n-x), with 0 < p < 1, x ≠ 0 or 7.
2. [A1] Correct expression, accept unsimplified, no terms omitted leading to final answer.
3. [B1] 0.647 < p < 0.6475
4. [M1] 1-p³, 0< p < 1, p = 1 – their (a), or correct.
5. [A1] 0.956
6. [B1] 48 and 9.6, 9 3/5, 48/5 seen, allow unsimplified. May be seen in the standardisation formula ([σ =] 3.098 < σ ≤ 3.1[0] implies correct variance). Incorrect notation penalised but values can be used as anticipated in remainder of question.
7. [M1] Substituting their μ and σ into ± standardising formula (any number for 46.5), not their σ² or √their σ.
8. [M1] Use continuity correction 46.5 or 47.5 in their standardised formula. Note: ±1.5/√9.6 or ±1.5/3.098 seen gains M2 BOD.
9. [M1] Appropriate area Φ, from final process, must be a probability. Expect final answer <0.5. Note: appropriate final answer implies this M1.
10. [A1] 0.314 < p < 0.3145