The times taken, in minutes, to complete a particular task by employees at a large company are normally distributed with mean 32.2 and standard deviation 9.6.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [M1] 28.6, 32.2 and 9.6 substituted appropriately in ± Standardisation formula once, allow continuity correction of ±0.05, no σ², √σ.
2. [M1] Appropriate numerical area, from final process, must be probability, expect > 0.5.
3. [A1] 0.646 AWRT
4. [B1] z = ±0.842
5. [M1] Substituting 32.2 and 9.6 into ± standardisation formula, no continuity correction, allow σ², √σ, must be equated to a z-value.
6. [A1] 40.28 < t < 40.3 WWW
7. [M1] Identifying at least one of 15/9.6 and -15/9.6 as the appropriate z-values or substituting their (32.2 ±15) into ± Standardisation formula once, no continuity correction, σ² nor √σ. Condone ±1.563 for M1.
8. [A1] p = 0.941 AWRT SOI
9. [M1] Appropriate area 2Φ – 1 oe, (eg 1 – 2 × 0.0591, 2 × (0.9409 – 0.5) or 0.9409 – 0.0591), from final process, must be probability > 0.5.
10. [A1] 0.882