A company sells small and large bags of rice. The masses of the small bags of rice are normally distributed with mean 1.20 kg and standard deviation 0.16 kg.

Mark scheme

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

1. [M1] Use of standardisation formula with 1.26, 1.20 and 0.16, not σ², not σ, no continuity correction.
2. [M1] Calculating the appropriate probability area, (leading to their final probability, expect < 0.5).
3. [A1] 0.3538, 0.3535 < p < 0.354. Only dependent on the 2nd M mark. SC B1 for 0.3535 < p < 0.354 if M0M0A0 awarded.
4. [B1 FT] Strict FT their at least 4-figure calculated probability, seen anywhere (not a z-value). Final answer must be a single positive integer value, no approximation or rounding stated.
5. [B1] -0.842 < z < -0.8415 or 0.8415 < z < 0.842 seen.
6. [M1] Use of the standardisation formula with 2.40, 2.50, σ and a z-value (not 0.20, 0.80, 0.158, 0.7881, 0.2119, 0.5793, 0.4207, ...), not σ². Condone continuity correction of ±0.005. Condone 0.1/σ = -0.842 etc. for M1.
7. [A1] 0.1185 < σ < 0.119.
8. [B1] 16 and 12.8 seen, allow unsimplified. May be seen in standardisation formula. 8√5 / 5, 3.5777... to at least three significant figures implies correct variance. Incorrect notation penalised.
9. [M1] Substituting their 16 (not 1.2, 2.5) and their 12.8 (not 0.16, their 0.119) in the standardising formula (any number for 21.5), condone σ² or √σ.
10. [M1] Using continuity correction 21.5 or 22.5 in their standardisation formula.
11. [M1] Appropriate area Φ, from final process, must be a probability.
12. [A1] 0.9375 < p < 0.938.