A-LevelMathematicsProbability and statistics9709/52 · May/June 2021 · Q24 Marks
The weights of bags of sugar are normally distributed with mean 1.04 kg and standard deviation σ kg. In a random sample of 2000 bags of sugar, 72 weighed more than 1.10 kg.
- Find the value of σ.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- B1 P(X>1.1)=72/2000 (=0.036), z = ±1.798 (1.79 < z < 1.80, -1.80 < z < -1.79 seen)
- B1 1.1 and 1.04 substituted in ±standardisation formula, allow continuity correction, not σ² or √σ
- M1 Equate their ±standardisation formula to a z-value and to solve for the appropriate area leading to final answer (expect σ < 0.5). (Accept ± 0.06/σ = z - value)
- A1 0.03335 ≤ σ ≤ 0.0334. At least 3 s.f.
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →