The time spent by shoppers in a large shopping centre has a normal distribution with mean 96 minutes and standard deviation 18 minutes.

Mark scheme

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

1. [1] M1 Use of standardisation formula once with appropriate values substituted, no continuity correction, not σ² or √σ.
2. [1] M1 Appropriate area Φ, from final process, must be probability. Use of (1 - z) implies M0.
3. [1] A1 Final answer which rounds to 0.317.
4. [1] B1 1.172 ≤ z ≤ 1·18 or −1·18 ≤ z ≤ −1·17
5. [1] M1 An equation using ±standardisation formula with a z-value, condone σ², √σ or continuity correction. E.g. equating to 0.88, 0·12, 0·8106, 0·1894, 0·5478, 0·4522, ±0·175 or ±2·175 implies M0.
6. [1] A1 74.85 < t < 74.9