In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m.

Mark scheme

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

1. [M1] Using ± standardisation formula with 1.93, 1.64 and 0.25 substituted, not σ², not √σ, no continuity correction.
2. [M1] Appropriate area Φ resulting from a standardisation, from final process, must be probability. Note: the appropriate probability answer implies this M1.
3. [A1] 0.123 < p < 0.12303 If M0 M0, SC B1 if no standardisation shown.
4. [B1] -0.441 < z1 < -0.439 or 0.439 < z1 < 0.441 seen.
5. [B1] z2 = 0.674 or z2 = - 0.674 seen, CAO, critical value.
6. [M1] Use of the standardisation formula once with μ, σ equating to a z-value (not 0.33, 0.67. 0.25, 0.75, 0.6293, 0.5987, 0.7486, 0.7734, (1-0.44), (1 – 0.674)). Condone continuity correct ±0.005, not σ², √σ.
7. [M1] Solve two equations in μ and σ using the elimination method, substitution method or other appropriate approach to obtain values for both μ and σ.
8. [A1] AWRT μ=1.68, σ = 0.269. If one or both of the M marks have not been awarded, SC B1 for both correct.