A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2023 · Q26 Marks

The weights of large bags of pasta produced by a company are normally distributed with mean 1.5kg and standard deviation 0.05 kg.

(a)Find the probability that a randomly chosen large bag of pasta weighs between 1.42kg and 1.52kg.[3]
(b)The weights of small bags of pasta produced by the company are normally distributed with mean 0.75 kg and standard deviation σkg. It is found that 68% of these small bags have weight less than 0.9kg. Find the value of σ.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[M1] Use of ± standardisation formula once with 1.5, 0.05 and either 1.42 or 1.52, allow σ² or √o, no continuity correction.
[M1] Calculating the appropriate probability area (leading to their final answer, expect > 0.5).
[A1] 0.6005 < p < 0.601 SC B1 for 0.601 with no standardisation seen.
[B1] 0.467 < z < 0.468 or -0.468 < z < -0.467 seen
[M1] standardisation formula with 0.9, 0.75, σ equating to a z-value (not 0.32, 0.68, 0.532, 0.7517, 0.2483, 0.6255,) . Condone continuity correct ±0.05, not σ², √o.
[A1] 0.3205 < σ < 0.3215 SC B1 if M0 www.

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.