Company A produces bags of sugar. An inspector finds that on average 10% of the bags are underweight. 10 of the bags are chosen at random. The weights of the bags of sugar produced by company B are normally distributed with mean 1.04 kg and standard deviation 0.06 kg. 81% of the bags of sugar produced by company B weigh less than w kg.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] One term ¹⁰Cx p^x (1-p)^(10-x), 0<p<1, x≠0
2. [A1] Correct expression, accept unsimplified.
3. [B1] 0.9298 < p < 0.9303
4. [M1] 1.11, 1.04 and 0.06 substituted into ±Standardisation formula, no continuity correction not 0.06² or √0.06
5. [M1] 1-their 0.8784 as final answer, must be probability. (Expect final ans < 0.5).
6. [A1] 0.1216 < p < 0.122 SC M0 M1 B1 for 0.122 with no standardisation formula.
7. [B1] 0.8775 < z < 0.878 or -0.878 < z < -0.8775 seen.
8. [M1] 1.04 and 0.06 substituted in standardisation formula, no continuity correction, not σ², √σ, equated to a z-value.
9. [A1] 1.09 ≤ w ≤ 1.093