The heights of the 124 Senior members of the Giraffes basketball club are normally distributed with mean 187.4 cm and standard deviation 6.4 cm. The heights of the Junior members of the Giraffes club are normally distributed with mean 172.7 cm and standard deviation σ cm. 23% of these members have height less than 170.3 cm.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [M1] Substituting 187.4 and 6.4 and either 182.4 or 192.4 appropriately into one standardising formula, allow σ² or √σ. Note 5/6.4 or -5/6.4 scores M1.
2. [M1] Appropriate area Φ, from final process. Must be a probability. There may be small variations in the probability values used – the values here are from the tables. Expect final answer > 0.5. Condone omission of brackets if recovered for their values.
3. [A1] 0.565 < p < 0.5655 SOI. If one or both M marks not awarded, SCB1 for 0.565 < p < 0.5655 SOI.
4. [B1FT] Strict FT their at least 4 figure probability × 124 (Check with calculator) One integer answer, expect 70 or 71. No indication of ‘approximation’, e.g. ≈, =, about, 2SF.
5. [B1] 0.7385 < z < 0.7395 or -0.7395 < z < -0.7385 seen.
6. [M1] standardisation formula with 170.3, 172.7, σ equated to a z-value (not 0.23, 0.77, 0.261, 0.591, 0.409, 0.7794, 0.2206, 1 – their z-value ...). Condone continuity correction ±0.05. Do not allow σ^2 or √σ. Condone ±2.4/σ = 0.739.
7. [A1] 3.245 < σ ≤ 3.25. Do not award for improper fractions. There must be consistency with signs in the solution, e.g. (172.7-170.3)/σ = -0.739, so σ = 3.25 is not acceptable, A0.