The weights of oranges can be modelled by a normal distribution with mean 131 grams and standard deviation 54 grams. Oranges are classified as small, medium or large. A large orange weighs at least 184 grams and 20% of oranges are classified as small.

Mark scheme

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

1. [M1] Use of standardisation formula with 184, 131 and 54, no continuity correction. Condone use of σ², √σ.
2. [M1] Calculating the appropriate probability area (leading to their final answer).
3. [A1] AWRT
4. [B1] -0.842 ≤ z ≤ -0.8415 or 0.8415 ≤ z ≤ 0.842 seen.
5. [M1] Use of the standardisation formula with 131, 54, w and a z-value (not 0.2, 0.8, 0.158, 0.508[0], 0.492[0], 0.7881, 0.2119, 0.5593, 0.4407).
6. [A1] 85.5 ≤ p ≤ 85.6 Signs must be consistent to create a positive answer.