The residents of Persham were surveyed about the reliability of their internet service. 12% rated the service as 'poor', 36% rated it as 'satisfactory' and 52% rated it as 'good'.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] One term ⁸Cₓ pˣ (1-p)⁸⁻ˣ, for 0 < x < 8, 0 < p < 1
2. [A1] Correct expression, accept unsimplified, no terms omitted, leading to final answer.
3. [B1] Mark the final answer at the most accurate value. 0.8248 < p < 0.825 WWW.
4. [B1] 65 and 31.2 seen, allow unsimplified. May be seen in standardisation formula. (5.585 < σ < 5.586 imply correct variance).
5. [M1] Substituting their 65 and √their31.2_into ±standardisation formula (any number for 72·5), not their 31.2, √ their 5.586 .
6. [M1] Using continuity correction 72.5 or 71·5 in their standardisation formula. Note ±7.5/√31.2 or ±7.5/5.586 seen gains M2 BOD
7. [M1] Appropriate area Φ, from final process, must be probability.
8. [A1] 0.0896 < p < 0.0897 WWW.