The heights of the female students at Breven college are normally distributed: • 90% of the female students have heights less than 182.7 cm. • 40% of the female students have heights less than 162.5 cm.

Mark scheme

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

1. [B1] 1.282 or –1.282 seen, CAO (critical value).
2. [B1] –0.2535 < z < –0.253 or 0.253 < z < 0.2535 seen.
3. [M1] One standardisation formula, not σ², or √σ, with 182.7 or 162.5 substituted correctly equated to a z value (not 0.9, 0.1, 0.8159, 0.5398, 0.4, 0.6, 0.6554, 0.7257, ...).
4. [M1] Either a single expression with one variable eliminated formed or two expressions with both variables on the same side seen with at least one variable value stated.
5. [A1] Answers must be to at least 1 DP (context).
6. [M1] One term ¹⁰Cₓ (p)ˣ (1–p)¹⁰⁻ˣ . With 0 < p < 1,x ≠ 0 or 10.
7. [A1] Correct unsimplified expression. Allow ¹⁰C₉. Condone omission of last bracket only. If both brackets omitted in unsimplified expression allow recovery for final stated calculation of 1 – 0.1673 or final answer WRT 0.8327.
8. [B1] 0.8327 < p < 0.833.