The heights, in metres, of white pine trees are normally distributed with mean 19.8 and standard deviation 2.4. In a certain forest there are 450 white pine trees.

Mark scheme

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

1. [M1] Use of ± standardisation formula with 18.2, 19.8 and 2.4 substituted appropriately, no continuity correction. Condone σ² (2.4²) or √(√2.4).
2. [M1] Calculating the appropriate probability areas (leading to their final answer, expect < 0.5). Note: 0.432 is z-value of 0.667 so is not an appropriate probability area (M0).
3. [A1] AWRT 0.252 SOI, accept 0.2525. If one or both M marks not awarded, SC B1 for AWRT 0.252 SOI, accept 0.2525.
4. [B1FT] Strict FT their at least 4 figure probability × 450. (Check with calculator). One integer answer only. No indication of 'approximation', e.g. ≈,=,about .
5. [B1] 0.643 ≤ z < 0.6435 or -0.6435 < z ≤ -0.643 seen.
6. [M1] ± standardisation formula with 25.5, 23.4, σ equating to a z-value, (not 1 – their z-value...). Condone continuity correction ±0.05, not σ², not √σ.
7. [Α1] 3.26 < σ < 3.27. Do not award for improper fractions.