The weights of the green apples sold by a shop are normally distributed with mean 90 grams and standard deviation 8 grams.

Mark scheme

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

1. [M1] Using ± standardisation formula with 90, 8 and either 83 or 95. Not σ², not σ, no continuity correction.
2. [A1] Both ±0.875 OE and ±0.625 OE seen. If M0 scored, SC B1 for both ±0.875 and ±0.625 seen
3. [M1] Calculating the appropriate probability area, leading to their final probability. Expect final answer > 0.5.
4. [A1] 0.5432, 0.543 < p < 0.5435. Only dependent on the 2nd M mark.
5. [B1] 96 and 38.4 seen, allow unsimplified. May be seen in the standardisation formula. 8√15/5 , 6.19677... to at least4 SF implies correct variance Withold mark if variance clearly identified as standard deviation, condone N(96, √38.4 ) if standardisation formula correct or variance/standard deviation correctly stated as well.
6. [M1] Substituting their 96 and their 38.4 into the standardising formula (any number for 104.5), condone σ² or √σ.
7. [M1] Use continuity correction 104.5 or 105.5 in their standardisation formula. Note: ±8.5/√38.4 or ±8.5/6.197 seen gains M2 BOD.
8. [M1] Appropriate area Φ, from final process, must be a probability. Expect final answer > 0.5.
9. [A1] 0.9149 < p < 0.915. If one or more M marks not scored, SC B1 for 0.9149 < p < 0.915.