A farmer sells eggs. The weights, in grams, of the eggs can be modelled by a normal distribution with mean 80.5 and standard deviation 6.6. Eggs are classified as small, medium or large according to their weight. A small egg weighs less than 76 grams and 40% of the eggs are classified as medium.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] Use of ± standardisation formula with 76, 80.5 and 6.6, condone 6.6² or √6.6, no continuity correction.
2. [M1] Calculating the appropriate probability area (leading to their final answer).
3. [A1] 24.75% < ans < 24.8% (percentage value required). If A0 scored, SC B1 for 24.75% < ans < 24.8% www.
4. [B1] 0.378 ≤ z < 0.3791 or -0.3791 < z < -0.378 seen.
5. [M1] Use of ± standardisation formula with x, 80.5, 6.6 and a z-value (not 0.6476, 0.3524, 0.4, 0.2476) (treat ±0.38 as a z-value), not 6.6², not √6.6, no continuity correction.
6. [A1] awrt 83.0
7. [B1] 60 and 36 seen, allow unsimplified.
8. [M1] Substituting their 60 and their 6 into ±standardisation formula (any number for 68.5), condone their σ² and their √σ.
9. [M1] Using continuity correction 67.5 or 68.5 in their standardisation formula.
10. [M1] Appropriate area Φ, from final process, must be a probability.
11. [A1] 0.07825 < p < 0.0783; If A0 scored, SC B1 for 0.07825 < p < 0.0783.