The residents of Mahjing were asked to classify their local bus service: * 25% of residents classified their service as good. * 60% of residents classified their service as satisfactory. * 15% of residents classified their service as poor.

Mark scheme

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

1. [B1] 27.5 and 20.625 (CAO) seen, allow unsimplified. May be in standardisation formula (4.541475... to at least 4sf or √165/8 or √330/4 implies correct variance). Penalise incorrect identification, condone no identification.
2. [M1] Substituting their 27.5 and their 20.625 into the standardising formula (any number for 21.5), not σ², not √σ.
3. [M1] Using continuity correction 21.5 or 22.5 in their standardisation formula.
4. [M1] Appropriate probability area, from final process, must be a probability. May be implied by a sketch of the required probability area. Expect final answer < 0.5.
5. [A1] 0.0932 ≤ p < 0.09325 If either M1 M1 not awarded for standardisation and/or M1 not awarded for finding probability area, SC B1 0.0932 ≤ p < 0.09325 WWW.
6. [M1] One term ¹⁰Cx (p)ˣ (1-p)¹⁰⁻ˣ, 0 < p < 1, x ≠ 0 or 10.
7. [A1] Correct unsimplified expression. Condone omission of last bracket only.
8. [B1] 0.1795 < p ≤ 0.180
9. [(M1)] One term ¹⁰Cx (p)ˣ (1-p)¹⁰⁻ˣ, 0 < p < 1, x ≠ 0 or 10.
10. [(A1)] Correct unsimplified expression.
11. [(B1)] 0.1795 < p < 0.180
12. [M1] 0.25 × 0.6 × 0.15 × k, k an integer > 1.
13. [A1]